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


SCHEDULE 13G
Under the Securities Exchange Act of 1934



Amendment No.: #3*


Name of Issuer: UAL Corporation 


Title of Class of Securities:  Common Stock


CUSIP Number:  90254950-0



*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).

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CUSIP No.: 90254950-0                            Page 2 of 8

1.  NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
         Janus Capital Corporation
         EIN #84-0765359

2.  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
         a.   ___
         b.   _X_

3.  SEC USE ONLY

4.  CITIZENSHIP OR PLACE OF ORGANIZATION
         Colorado

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:

    5.   SOLE VOTING POWER
              -0-  

    6.   SHARED VOTING POWER
              1,805,585**    
    
    7.   SOLE DISPOSITIVE POWER
              -0-

    8.   SHARED DISPOSITIVE POWER
              1,805,585**

9.  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         1,805,585**

10. CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
         N/A
         
11. PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
         3.1%**

12. TYPE OF REPORTING PERSON
         IA, CO

**  See Item 4 of this filing

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CUSIP No.:  90254950-0                           Page 3 of 8

1.  NAME OF REPORTING PERSON
         S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
         Thomas H. Bailey

2.  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
         a.   ___
         b.   _X_

3.  SEC USE ONLY   

4.  CITIZENSHIP OR PLACE OF ORGANIZATION
         USA

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:

    5.   SOLE VOTING POWER
              -0-

    6.   SHARED VOTING POWER
              1,805,585**

    7.   SOLE DISPOSITIVE POWER
              -0-

    8.   SHARED DISPOSITIVE POWER
              1,805,585**

9.  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
         1,805,585**

10. CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES
         N/A

11. PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
         3.1%**

12. TYPE OF REPORTING PERSON
         IN
**  See Item 4 of this filing


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SCHEDULE 13G                                          Page 4 of 8

Item 1.

    (a). Name of Issuer: UAL Corporation ("UAL Corp.")
    
    (b). Address of Issuer's Principal Executive Offices:

         1200 E. Algonquin Rd.
         Elk Grove Township, IL 60007

Item 2.

    (a).-(c). Name, Principal Business Address, and Citizenship of Persons
              Filing:

         (1)  Janus Capital Corporation ("Janus Capital")
              100 Fillmore Street
              Denver, Colorado  80206-4923
              Citizenship:  Colorado

         (2)  Thomas H. Bailey ("Mr. Bailey")
              100 Fillmore Street
              Denver, Colorado  80206-4923
              Citizenship:  USA
         
    (d). Title of Class of Securities:  Common Stock 

    (e). CUSIP Number:  90254950-0

Item 3.  

    Janus Capital is an Investment Adviser registered under Section 203 of the
    Investment Advisers Act of 1940.


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SCHEDULE 13G                                          Page 5 of 8

Item 4.  Ownership

         The information in items 1 and 5 through 11 on the cover pages (pp. 2-
         3) on Schedule 13G is hereby incorporated by reference.

         Janus Capital is a registered investment adviser which furnishes
         investment advice to several investment companies registered under
         Section 8 of the Investment Company Act of 1940 and individual and
         institutional clients (collectively referred to herein as "Managed
         Portfolios").  As a result of its role as investment adviser or sub-
         adviser to the Managed Portfolios, Janus Capital may be deemed to be
         the beneficial owner of the shares of UAL Corp. Common Stock held by
         such Managed Portfolios.  However, Janus Capital does not have the
         right to receive any dividends from, or the proceeds from the sale of,
         the securities held in the Managed Portfolios and disclaims any
         ownership associated with such rights.

         Mr. Bailey owns approximately 12.2% of Janus Capital.  In addition to
         being a stockholder of Janus Capital, Mr. Bailey serves as President
         and Chairman of the Board of Janus Capital and is filing this joint
         statement with Janus Capital as a result of such stock ownership and
         positions which may be deemed to enable him to exercise control over
         Janus Capital.  Mr. Bailey does not own of record any shares of UAL
         Corp. Common Stock and he has not engaged in any transaction in UAL
         Corp. Common Stock.  However, as a result of his position, Mr. Bailey
         may be deemed to have the power to exercise or to direct the exercise
         of such voting and/or dispositive power that Janus Capital may have
         with respect to UAL Corp. Common Stock held by the Managed Portfolios. 
         All shares reported herein have been acquired by the Managed
         Portfolios, and Mr. Bailey specifically disclaims beneficial ownership
         over any shares of UAL Corp. Common Stock that he or Janus Capital may
         be deemed to beneficially own.  Furthermore, Mr. Bailey does not have
         the right to receive any dividends from, or the proceeds from the sale
         of, the securities held in the Managed Portfolios and disclaims any
         ownership associated with such rights.
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SCHEDULE 13G                                          Page 6 of 8

Item 5.  Ownership of Five Percent or Less of a Class
                             
              This statement is being filed to report the fact that the
              reporting persons have ceased to be the beneficial owners of more
              than five percent of the class of securities.

              These shares were acquired in the ordinary course of business,
              and not with the purpose of changing or influencing control of
              the Issuer.

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 Reported on by the Parent Holding
         Company

              N/A

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.


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SCHEDULE 13G                                          Page 7 of 8

SIGNATURES                                            

    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.


JANUS CAPITAL CORPORATION

By  /s/  Deborah E. Bielicke                       6/9/98    
   Deborah E. Bielicke                              Date

   Under Power of Attorney dated 6/30/97            
   On File with Schedule 13G for
   CommNet Cellular, Inc. 7/9/97                    


THOMAS H. BAILEY

By  /s/  Deborah E. Bielicke                       6/9/98   
   Deborah E. Bielicke                               Date

   Under Power of Attorney dated 6/30/97
   On File with Schedule 13G for
   CommNet Cellular, Inc. 7/9/97      


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SCHEDULE 13G                                        Page 8 of 8

EXHIBIT A


JOINT FILING AGREEMENT


  In accordance with Rule 13d-1(f) under the Securities Exchange Act of 1934,
the persons named below agree to the joint filing on behalf of each of them
of a Statement on Schedule 13G (including amendments thereto) with respect to
the Common Stock of UAL Corporation and further agree that this Joint Filing
Agreement be included as an Exhibit to such joint filings.  In evidence
thereof, the undersigned hereby execute this Agreement as of the 9th day of
June, 1998.


            JANUS CAPITAL CORPORATION

            By  /s/  Deborah E. Bielicke            
               Deborah E. Bielicke

               Under Power of Attorney dated 6/30/97  
               On File with Schedule 13G for
               CommNet Cellular, Inc. 7/9/97


            THOMAS H. BAILEY
            
            By  /s/  Deborah E. Bielicke                
               Deborah E. Bielicke

               Under Power of Attorney dated 6/30/97  
               On File with Schedule 13G for
               CommNet Cellular, Inc. 7/9/97