Page 1 of 13 Pages

                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C.  20549

                                  SCHEDULE 13G

                    Under the Securities Exchange Act of 1934

                             (AMENDMENT NO.6)*

                              CONTINENTAL AIRLS INC
            ------------------------------------------------------
                                (NAME OF ISSUER)

                                  Common Stock Cl B
            ------------------------------------------------------
                         (TITLE OF CLASS OF SECURITIES)

                                  210795308
            ------------------------------------------------------
                                (CUSIP NUMBER)

                                  December 31, 1998
            ------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)

      Check the appropriate box to designate the rule pursuant to which
      this Schedule is filed:

      X  Rule 13d-1(b)
      -
         Rule 13d-1(c)
      -
         Rule 13d-1(d)
      -

    * The remainder of this cover page shall be filled out for a reporting
    person`s initial filing on this form with respect to the subject class
    of securities, and for any subsequent amendment containing information
    which would alter the disclosures provided in a prior cover page.

    The information required in the remainder of this cover page shall not
    be deemed to be 'filed' for the purpose of Section 18 of the Securities
    Exchange Act of 1934 ('Act') or otherwise subject to the liabilities
    of that section of the Act but shall be subject to all other provisions
    of the Act (however, see the Notes).

                       (CONTINUED ON FOLLOWING PAGE(S))

<PAGE>


    --------------------                          --------------------
    CUSIP NO. 210795308          13G               Page 2 of 13 Pages
    --------------------                          --------------------
    --------------------------------------------------------------------
     1- NAME OF REPORTING PERSON
      AXA Assurances I.A.R.D. Mutuelle

      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    -------------------------------------------------------------------
     2- CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP *   (A) [ ]
                                                             (B) [X]
    -------------------------------------------------------------------
     3- SEC USE ONLY


    -------------------------------------------------------------------
     4- CITIZENSHIP OR PLACE OF ORGANIZATION

      France
    -------------------------------------------------------------------
    NUMBER OF SHARES BENEFICIALLY OWNED
    AS OF December 31, 1998 BY EACH REPORTING PERSON WITH
                -----------------------------------------------
                5- SOLE VOTING POWER
                     7,326,337
                -----------------------------------------------
                6- SHARED VOTING POWER
                     8,255,300
                -----------------------------------------------
                7- SOLE DISPOSITIVE POWER
                     18,148,029
                -----------------------------------------------
                8- SHARED DISPOSITIVE POWER
                     400
    --------------------------------------------------------------------
     9- AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                18,148,429
      (Not to be construed as an admission of beneficial ownership)
    -------------------------------------------------------------------
    10- CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
      SHARES *                                            |------|
                                                          |------|
    -------------------------------------------------------------------
    11- PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                         37.7%
    -------------------------------------------------------------------
    12- TYPE OF REPORTING PERSON *

                                   IC
    --------------------------------------------------------------------

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>

    --------------------                          --------------------
    CUSIP NO. 210795308          13G               Page 3 of 13 Pages
    --------------------                          --------------------
    --------------------------------------------------------------------
     1- NAME OF REPORTING PERSON
      AXA Assurances Vie Mutuelle

      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    -------------------------------------------------------------------
     2- CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP *   (A) [ ]
                                                             (B) [X]
    -------------------------------------------------------------------
     3- SEC USE ONLY


    -------------------------------------------------------------------
     4- CITIZENSHIP OR PLACE OF ORGANIZATION

      France
    --------------------------------------------------------------------
    NUMBER OF SHARES BENEFICIALLY OWNED
    AS OF December 31, 1998 BY EACH REPORTING PERSON WITH
                -----------------------------------------------
                5- SOLE VOTING POWER
                     7,326,337
                -----------------------------------------------
                6- SHARED VOTING POWER
                     8,255,300
                -----------------------------------------------
                7- SOLE DISPOSITIVE POWER
                     18,148,029
                -----------------------------------------------
                8- SHARED DISPOSITIVE POWER
                     400
    --------------------------------------------------------------------
     9- AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                18,148,429
      (Not to be construed as an admission of beneficial ownership)
    -------------------------------------------------------------------
    10- CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
      SHARES *                                            |------|
                                                          |------|
    -------------------------------------------------------------------
    11- PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                         37.7%
    -------------------------------------------------------------------
    12- TYPE OF REPORTING PERSON *

                                   IC
    --------------------------------------------------------------------

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>

    --------------------                          --------------------
    CUSIP NO. 210795308          13G               Page 4 of 13 Pages
    --------------------                          --------------------
    --------------------------------------------------------------------
     1- NAME OF REPORTING PERSON
      AXA Conseil Vie Assurance Mutuelle
          (formerly Alpha Assurances Vie Mutuelle)
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    -------------------------------------------------------------------
     2- CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP *   (A) [ ]
                                                             (B) [X]
    -------------------------------------------------------------------
     3- SEC USE ONLY


    -------------------------------------------------------------------
     4- CITIZENSHIP OR PLACE OF ORGANIZATION

      France
    --------------------------------------------------------------------
    NUMBER OF SHARES BENEFICIALLY OWNED
    AS OF December 31, 1998 BY EACH REPORTING PERSON WITH
                -----------------------------------------------
                5- SOLE VOTING POWER
                     7,326,337
                -----------------------------------------------
                6- SHARED VOTING POWER
                     8,255,300
                -----------------------------------------------
                7- SOLE DISPOSITIVE POWER
                     18,148,029
                -----------------------------------------------
                8- SHARED DISPOSITIVE POWER
                     400
    --------------------------------------------------------------------
     9- AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                18,148,429
      (Not to be construed as an admission of beneficial ownership)
    -------------------------------------------------------------------
    10- CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
      SHARES *                                            |------|
                                                          |------|
    -------------------------------------------------------------------
    11- PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                        37.7%
    -------------------------------------------------------------------
    12- TYPE OF REPORTING PERSON *

                                   IC
    --------------------------------------------------------------------

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>

    --------------------                          --------------------
    CUSIP NO. 210795308         13G                Page 5 of 13 Pages
    --------------------                          --------------------
    --------------------------------------------------------------------
     1- NAME OF REPORTING PERSON
      AXA Courtage Assurance Mutuelle

      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    -------------------------------------------------------------------
     2- CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP *   (A) [ ]
                                                             (B) [X]
    -------------------------------------------------------------------
     3- SEC USE ONLY


    -------------------------------------------------------------------
     4- CITIZENSHIP OR PLACE OF ORGANIZATION

      France
    --------------------------------------------------------------------
    NUMBER OF SHARES BENEFICIALLY OWNED
    AS OF December 31, 1998 BY EACH REPORTING PERSON WITH
                -----------------------------------------------
                5- SOLE VOTING POWER
                     7,326,337
                -----------------------------------------------
                6- SHARED VOTING POWER
                     8,255,300
                -----------------------------------------------
                7- SOLE DISPOSITIVE POWER
                     18,148,029
                -----------------------------------------------
                8- SHARED DISPOSITIVE POWER
                     400
    --------------------------------------------------------------------
     9- AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                18,148,429
      (Not to be construed as an admission of beneficial ownership)
    -------------------------------------------------------------------
    10- CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
      SHARES *                                            |------|
                                                          |------|
    -------------------------------------------------------------------
    11- PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                     37.7%
    -------------------------------------------------------------------
    12- TYPE OF REPORTING PERSON *

                                   IC
    --------------------------------------------------------------------

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>

    --------------------                          --------------------
    CUSIP NO. 210795308          13G               Page 6 of 13 Pages
    --------------------                          --------------------
    --------------------------------------------------------------------
     1- NAME OF REPORTING PERSON
      AXA  (formerly AXA-UAP)

      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

    -------------------------------------------------------------------
     2- CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP *   (A) [ ]
                                                             (B) [ ]
    -------------------------------------------------------------------
     3- SEC USE ONLY


    -------------------------------------------------------------------
     4- CITIZENSHIP OR PLACE OF ORGANIZATION

      France
    --------------------------------------------------------------------
    NUMBER OF SHARES BENEFICIALLY OWNED
    AS OF December 31, 1998 BY EACH REPORTING PERSON WITH
                -----------------------------------------------
                5- SOLE VOTING POWER
                     7,326,337
                -----------------------------------------------
                6- SHARED VOTING POWER
                     8,255,300
                -----------------------------------------------
                7- SOLE DISPOSITIVE POWER
                     18,148,029
                -----------------------------------------------
                8- SHARED DISPOSITIVE POWER
                     400
    --------------------------------------------------------------------
     9- AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                18,148,429
      (Not to be construed as an admission of beneficial ownership)
    -------------------------------------------------------------------
    10- CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
      SHARES *                                            |------|
                                                          |------|
    -------------------------------------------------------------------
    11- PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                             37.7%
    -------------------------------------------------------------------
    12- TYPE OF REPORTING PERSON *

                                   HC
    --------------------------------------------------------------------

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>

    --------------------                          --------------------
    CUSIP NO. 210795308          13G               Page 7 of 13 Pages
    --------------------                          --------------------
    --------------------------------------------------------------------
     1- NAME OF REPORTING PERSON
      THE EQUITABLE COMPANIES INCORPORATED

      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
      13-3623351
    -------------------------------------------------------------------
     2- CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP *   (A) [ ]
                                                             (B) [ ]
    -------------------------------------------------------------------
     3- SEC USE ONLY


    -------------------------------------------------------------------
     4- CITIZENSHIP OR PLACE OF ORGANIZATION

      State of Delaware
    --------------------------------------------------------------------
    NUMBER OF SHARES BENEFICIALLY OWNED
    AS OF December 31, 1998 BY EACH REPORTING PERSON WITH
                -----------------------------------------------
                5- SOLE VOTING POWER
                     7,326,037
                -----------------------------------------------
                6- SHARED VOTING POWER
                     8,255,300
                -----------------------------------------------
                7- SOLE DISPOSITIVE POWER
                     18,147,729
                -----------------------------------------------
                8- SHARED DISPOSITIVE POWER
                     400
    --------------------------------------------------------------------
     9- AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                18,148,129

    -------------------------------------------------------------------
    10- CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
      SHARES *                                            |------|
                                                          |------|
    -------------------------------------------------------------------
    11- PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

                 37.7%
    -------------------------------------------------------------------
    12- TYPE OF REPORTING PERSON *

                                  HC
    --------------------------------------------------------------------

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>

    Item 1(a) Name of Issuer:                         Page 8 of 13 Pages
              --------------
              CONTINENTAL AIRLS INC

    Item 1(b) Address of Issuer's Principal Executive Offices:
              -----------------------------------------------
              2929 Allen Pkwy.
              Houston, TX 77019


    Item 2(a) Name of Person Filing:
              ---------------------
              AXA Conseil Vie Assurance Mutuelle,
                  (formerly Alpha Assurances Vie Mutuelle)
              AXA Assurances I.A.R.D Mutuelle,
              AXA Assurances Vie Mutuelle,
              and AXA Courtage Assurance Mutuelle,
              as a group (collectively, the 'Mutuelles AXA').

              AXA  (formerly AXA-UAP)

              The Equitable Companies Incorporated
                (the 'Equitable Companies')

                (Please contact Patrick Meehan at (212) 641-8234
                            with any questions.)

    Item 2(b) Address of Principal Business Office:
              ------------------------------------
              AXA Conseil Vie Assurance Mutuelle
              100-101 Terrasse Boieldieu
              92042 Paris La Defense France

              AXA Assurances I.A.R.D Mutuelle and
              AXA Assurances Vie Mutuelle
              21, rue de Chateaudun
              75009 Paris France

              AXA Courtage Assurance Mutuelle
              26, rue Louis le Grand
              75002 Paris France

              AXA
              9 Place Vendome
              75001 Paris France

              The Equitable Companies Incorporated
              1290 Avenue of the Americas
              New York, New York 10104



<PAGE>

                                                      Page  9 of 13 Pages


    Item 2(c) Citizenship:
              -----------
              Mutuelles AXA and AXA France
              Equitable Companies - Delaware

    Item 2(d) Title of Class of Securities:
              ----------------------------
              Common Stock Cl B

    Item 2(e) CUSIP Number:
              ------------
              210795308

    Item 3.   Type of Reporting Person:
              ------------------------
              Equitable Companies as a parent holding company,
              in accordance with 240.13d-1 (b)(ii)(G).

              The Mutuelles AXA, as a group, acting as a parent
              holding company.

              AXA as a parent holding company.

<PAGE>



<TABLE>
                                                    Page 10 of 13 Pages
    Item 4. Ownership as of December 31, 1998:
            ------------------------------
    (a) Amount Beneficially Owned:
        -------------------------
       18,148,429 shares of common stock beneficially owned including:
<CAPTION>
                                                        No. of Shares
                                                    ---------------------
    <S>                                          <C>          <C>
    The Mutuelles AXA, as a group                                       0
    AXA                                                                 0
    AXA Entity or Entities:
       AXA Colonia Konzern AG (Germany)
    Common Stock                                         300          300
                                                  ----------
        acquired solely for investment purposes:

    (Each of the Mutuelles AXA, as a group, and AXA expressly declares
    that the filing of this Schedule 13G shall not be construed as an
    admission that it is, for purposes of Section 13(d) of the Exchange Act,
    the beneficial owner of any securities covered by this Schedule 13G).

    <S>                                          <C>          <C>
    The Equitable Companies Incorporated                                0

    Subsidiaries:
    ------------

    Alliance Capital Management L.P.
    acquired solely for investment purposes on
    behalf of client discretionary investment
    advisory accounts:
    Common Stock                                  14,376,832   14,376,832
                                                  ----------
    Donaldson, Lufkin & Jenrette Securities Corporation
    held for investment purposes:
    Common Stock                                         400          400
                                                  ----------
    The Equitable Life Assurance Society of the United States
    acquired solely for investment purposes:
    Common Stock                                   3,770,597    3,770,597
                                                  ----------
    Wood, Struthers & Winthrop Management Corporation
    acquired solely for investment purposes on
    behalf of client discretionary investment
    advisory accounts:
    Common Stock                                         300          300
                                                  ----------

                                                              -----------
    Total                                                      18,148,429
                                                              ===========
    (Each of the above subsidiaries of The Equitable operates under
    independent management and makes independent decisions.)
    <S>                                                           <C>

    (b) Percent of Class:                                        37.7%
        ----------------                                      ===========
</TABLE>


<PAGE>


<TABLE>
    ITEM 4. Ownership as of 12/31/98(CONT.)   Page 11 of 13 Pages

       (c) Deemed Voting Power and Disposition Power:
           -----------------------------------------
<CAPTION>
                         (i)         (ii)          (iii)        (iv)
                        Deemed        Deemed        Deemed       Deemed
                        to have       to have       to have      to have
                        Sole Power    Shared Power  Sole Power   Shared Power
                        to Vote       to Vote       to Dispose   to Dispose
                        or to         or to         or to        or to
                        Direct        Direct        Direct the   Direct the
                        the Vote      the Vote      Disposition  Disposition
                        ------------  ------------  ------------ ------------

    <S>                 <C>           <C>           <C>          <C>
    The Mutuelles AXA,
        as a group               0             0             0             0

    AXA                          0             0             0             0

    AXA Entity
    or Entities:
    ------------------
    AXA Colonia Konzern AG
    (Germany)
                               300             0           300             0


    The Equitable
    Companies
    Incorporated                 0             0             0             0

    Subsidiaries:
    ------------
    Alliance Capital
    Management L.P.
                         3,716,040     8,094,700    14,376,832             0
    Donaldson, Lufkin
    & Jenrette
    Securities
    Corporation
                                 0             0             0           400
    The Equitable
    Life Assurance
    Society of the
    United States
                         3,609,997       160,600     3,770,597             0
    Wood, Struthers
    & Winthrop
    Management
    Corporation
                                 0             0           300             0

                      ------------  ------------  ------------  ------------
               TOTAL     7,326,337     8,255,300    18,148,029           400
                      ============  ============  ============  ============

  (Each of the above subsidiaries of the Equitable Companies operates under
  independent management and makes independent voting and investment
  decisions).

</TABLE>



<PAGE>

                                                      Page 12 of 13 Pages
    Item 5.
     Ownership of Five Percent or Less of a Class:
     ---------------------------------------------
     If this statement is being filed to report the fact that as of the date
     hereof the reporting person has ceased to be the beneficial owner of
     more than five percent of the class of securities, check the following.
                                                            ( )
    Item 6.
     Ownership of More than Five Percent on behalf of Another Person.  N/A
     ----------------------------------------------------------------
    Item 7.
     Identification and Classification of the Subsidiary which Acquired
     ------------------------------------------------------------------
     the Security Being Reporting on by the Parent Holding Company:
     -------------------------------------------------------------

     This Schedule 13G is being filed by Equitable Companies; AXA,
     which beneficially owns a majority interest in Equitable Companies;
     and the Mutuelles AXA, which as a group control AXA:

    (X)  in the Mutuelles AXAs' capacity, as a group, acting as a parent
         holding company with respect to the holdings of the following
         AXA entity or entities;

    (X)  in AXA's capacity as a parent holding company with respect
         to the holdings of the following AXA entity or entities:
          AXA Colonia Konzern AG (Germany)

    (X)  in EQUITABLE COMPANIES capacity as a parent holding company
         with respect to the holdings of its following subsidiaries:

    (X)  Alliance Capital Management L.P.
         (13-3434400),  an investment adviser registered under Section
         203 of the Investment Advisers Act of 1940.
    (X)  Donaldson, Lufkin & Jenrette Securities Corporation
         (13-2741729), a broker-dealer registered under Section 15 of
         the Securities and Exchange Act of 1934 and an investment
         adviser registered under Section 203 of the Investment
         Advisers Act of 1940.
    (X)  The Equitable Life Assurance Society of the United States
         (13-5570651), an insurance company, a broker-dealer registered
         under Section 15 of the Securities and Exchange Actof 1934
         and an investment adviser registered under Section 203 of the
         Investment Advisers Act of 1940.
    (X)  Wood, Struthers & Winthrop Management Corporation
         (13-2774791), an investment adviser registered under Section
         203 of the Investment Advisers Act of 1940.


<PAGE>

                                                      Page 13 of 13 Pages

    Item 8. Identification and Classification of Members of the Group.  N/A
            ---------------------------------------------------------

    Item 9.  Notice of Dissolution of Group:  N/A
             ------------------------------

    Item 10. Certification:
             -------------
         By signing below I certify that to the best of my knowledge and
    belief, the securities referred to above were acquired in the ordinary
    course of business and were not acquired for the purpose of and do not
    have the effect of changing or influencing the control of the issuer
    of such securities and were not acquired in connection with or as a
    participant in any transaction having such purposes or effect.



         Signature
         ---------
         After reasonable inquiry and to the best of my knowledge and
    belief, I certify that the information set forth in this statement
    is true, complete and correct.





    Date: February 10, 1999   THE EQUITABLE COMPANIES INCORPORATED*




                                            /s/ Alvin H. Fenichel
                             --------------------------------------------
                                           Alvin H. Fenichel
                                         Senior Vice President
                                            and Controller



    *Pursuant to the Joint Filing Agreement with respect to Schedule 13G
    attached hereto as Exhibit I, among The Equitable Companies Incorporated,
    AXA Conseil Vie Assurance Mutuelle, AXA Assurances I.A.R.D Mutuelle, AXA
    Assurances Vie Mutuelle, AXA Courtage Assurance Mutuelle, and AXA,
    this statement Schedule 13G is filed on behalf of each of them.







                                                                 EXHIBIT I



                                   JOINT FILING AGREEMENT
                                   ----------------------




                       Each of the undersigned hereby agrees that the
               Schedule 13G filed herewith is filed jointly, pursuant to
               Rule 13d-1(f)(1) of the Securities Exchange Act of 1934,
               as amended on behalf of each of them.


               Dated: February 10, 1999



               The Equitable Companies Incorporated



               BY:  /s/ Alvin H. Fenichel
                  -------------------------
                  Alvin H. Fenichel
                  Senior Vice President
                  and Controller



               AXA Assurances I.A.R.D. Mutuelle; AXA Assurances Vie Mutuelle;
               AXA Conseil Vie Assurance Mutuelle; AXA Courtage Assurance
               Mutuelle, as a group, and AXA

               Signed on behalf of each of the above entities



               BY:      /s/ Alvin H. Fenichel
                  -----------------------------------------
                  Alvin H. Fenichel
                  Attorney-in-Fact
                  (Executed pursuant to Powers of Attorney)