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.15)*

                               UAL CORP
            ------------------------------------------------------
                                (NAME OF ISSUER)

                                  COM PAR $0.01
            -----------------------------------------------------
                         (TITLE OF CLASS OF SECURITIES)

                                 902549500
            -----------------------------------------------------
                                (CUSIP NUMBER)

                                  December 31, 2000
            -----------------------------------------------------
            (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. 902549500          13G                         Page 2 of 13 Pages

  1. NAME OF REPORTING PERSON
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

        AXA Assurances I.A.R.D. Mutuelle

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


  4. CITIZENSHIP OR PLACE OF ORGANIZATION
        France

   NUMBER OF SHARES     5.  SOLE VOTING POWER                 3,650,540
    BENEFICIALLY
     OWNED AS OF        6.  SHARED VOTING POWER               7,216,200
  December 31, 2000
       BY EACH          7.  SOLE DISPOSITIVE POWER            14,950,040
      REPORTING
     PERSON WITH:       8.  SHARED DISPOSITIVE POWER          0

  9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
     REPORTING PERSON                                         14,950,040
        (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          28.7%

 12. TYPE OF REPORTING PERSON *
          IC

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>
CUSIP NO. 902549500          13G                             Page 3 of 13 Pages

  1. NAME OF REPORTING PERSON
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

        AXA Assurances Vie Mutuelle

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


  4. CITIZENSHIP OR PLACE OF
        France

   NUMBER OF SHARES     5.  SOLE VOTING POWER                 3,650,540
    BENEFICIALLY
     OWNED AS OF        6.  SHARED VOTING POWER               7,216,200
  December 31, 2000
       BY EACH          7.  SOLE DISPOSITIVE POWER            14,950,040
      REPORTING
     PERSON WITH:       8.  SHARED DISPOSITIVE POWER          0

  9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
     REPORTING PERSON                                         14,950,040
        (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          28.7%

 12. TYPE OF REPORTING PERSON *
          IC

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>
    CUSIP NO. 902549500          13G                         Page 4 of 13 Pages

  1. NAME OF REPORTING PERSON
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

        AXA Conseil Vie Assurance Mutuelle

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


  4. CITIZENSHIP OR PLACE OF ORGANIZATION
        France

   NUMBER OF SHARES     5.  SOLE VOTING POWER                 3,650,540
    BENEFICIALLY
     OWNED AS OF        6.  SHARED VOTING POWER               7,216,200
  December 31, 2000
       BY EACH          7.  SOLE DISPOSITIVE POWER            14,950,040
      REPORTING
     PERSON WITH:       8.  SHARED DISPOSITIVE POWER          0

  9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
     REPORTING PERSON                                         14,950,040
        (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          28.7%

 12. TYPE OF REPORTING PERSON *
          IC

                  * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>
    CUSIP NO. 902549500         13G                          Page 5 of 13 Pages

  1. NAME OF REPORTING PERSON
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

        AXA Courtage Assurance Mutuelle

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


  4. CITIZENSHIP OR PLACE OF ORGANIZATION
        France

   NUMBER OF SHARES     5.  SOLE VOTING POWER                 3,650,540
    BENEFICIALLY
     OWNED AS OF        6.  SHARED VOTING POWER               7,216,200
  December 31, 2000
       BY EACH          7.  SOLE DISPOSITIVE POWER            14,950,040
      REPORTING
     PERSON WITH:       8.  SHARED DISPOSITIVE POWER          0

  9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
     REPORTING PERSON                                         14,950,040
        (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          28.7%

 12. TYPE OF REPORTING PERSON *
          IC

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>
    CUSIP NO. 902549500          13G                         Page 6 of 13 Pages

  1. NAME OF REPORTING PERSON
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

          AXA

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


  4. CITIZENSHIP OR PLACE OF ORGANIZATION
        France

   NUMBER OF SHARES     5.  SOLE VOTING POWER                 3,650,540
    BENEFICIALLY
     OWNED AS OF        6.  SHARED VOTING POWER               7,216,200
  December 31, 2000
       BY EACH          7.  SOLE DISPOSITIVE POWER            14,950,040
      REPORTING
     PERSON WITH:       8.  SHARED DISPOSITIVE POWER          0

  9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
     REPORTING PERSON                                         14,950,040
        (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          28.7%

 12. TYPE OF REPORTING PERSON *
          HC

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>
    CUSIP NO. 902549500          13G                         Page 7 of 13 Pages

     1. NAME OF REPORTING PERSON
        I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

           AXA FINANCIAL, INC.          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     5.  SOLE VOTING POWER                 3,650,540
    BENEFICIALLY
     OWNED AS OF        6.  SHARED VOTING POWER               7,216,200
  December 31, 2000
       BY EACH          7.  SOLE DISPOSITIVE POWER            14,950,040
      REPORTING
     PERSON WITH:       8.  SHARED DISPOSITIVE POWER          0

  9. AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH
     REPORTING PERSON                                         14,950,040
        (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          28.7%

 12. TYPE OF REPORTING PERSON *
          HC

                    * SEE INSTRUCTIONS BEFORE FILLING OUT!


<PAGE>
                                                           Page 8 of 13 Pages
Item 1(a) Name of Issuer:
          UAL CORP

Item 1(b) Address of Issuer's Principal Executive Offices:
          1200 E Algonquin Road
          Elk Grove Vill, IL 60007


Item 2(a) and (b)
          Name of Person Filing and Address of Principal Business Office:

          AXA Conseil Vie Assurance Mutuelle,
          AXA Assurances I.A.R.D Mutuelle, and
          AXA Assurances Vie Mutuelle
          370, rue Saint Honore
          75001 Paris, France

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

          as a group (collectively, the 'Mutuelles AXA').

          AXA
          25, avenue Matignon
          75008 Paris, France

          AXA Financial, Inc.
          1290 Avenue of the Americas
          New York, New York 10104

          (Please contact Patrick Meehan at (212) 314-5644 with any questions.)

<PAGE>
                                                           Page  9 of 13 Pages
Item 2(c) Citizenship:
          Mutuelles AXA and AXA - France
          AXA Financial, Inc. - Delaware

Item 2(d) Title of Class of Securities:
          COM PAR $0.01

Item 2(e) CUSIP Number:
          902549500

Item 3.   Type of Reporting Person:
          AXA Financial, Inc. 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, 2000:
(a) Amount Beneficially Owned:

   14,950,040 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 Financial, Inc.                                                     0

Subsidiaries:

Alliance Capital Management L.P.
acquired solely for investment purposes on
behalf of client discretionary investment
advisory accounts:
    Common Stock                                  14,950,040   14,950,040
                                                  ----------  -----------
    Total                                                      14,950,040
                                                              ===========
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.

Each of the above subsidiaries of AXA Financial, Inc. operates under
independent management and makes independent decisions.
<S>                                                              <C>

    (b) Percent of Class:                                        28.7%
                                                              ===========
</TABLE>


<PAGE>

<TABLE>
    ITEM 4. Ownership as of 12/31/2000(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:
------------
    NONE

AXA Financial, Inc.              0             0             0             0

Subsidiaries:
-------------
Alliance Capital
Management L.P.
                         3,650,540     7,216,200    14,950,040             0
                      ------------  ------------  ------------  ------------
               TOTAL     3,650,540     7,216,200    14,950,040             0
                      ============  ============  ============  ============

Each of the above subsidiaries of the AXA Financial, Inc. 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 AXA Financial, Inc.; AXA,
        which beneficially owns a majority interest in AXA Financial, Inc.;
        and the Mutuelles AXA, which as a group control AXA:

    ( )  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;

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

    (X)  in AXA Financial, Inc.'s 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.


<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 12, 2001                 AXA FINANCIAL, INC.*

                                        /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 AXA Financial, Inc.,
    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 13d-1(f)(1) of the
          Securities Exchange Act of 1934, as amended on behalf of each of them.


               Dated: February 12, 2001

               AXA Financial, Inc.



               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)