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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                    FORM 8-K

                                 CURRENT REPORT
                         Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934


          Date of Report (Date of earliest event reported): May 6, 1999




                                EXXON CORPORATION
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             (Exact Name of Registrant as Specified in its Charter)



          New Jersey                       1-2256                13-5409005
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(State or Other Jurisdiction of   (Commission File Number)     (IRS Employer
        Incorporation)                                       Identification No.)




             5959 Las Colinas Boulevard                    
                    Irving, Texas                               75039-2298      
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      (Address of Principal Executive Offices)                  (Zip Code) 
                                                           




                                 (972) 444-1000
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              (Registrant's telephone number, including area code)




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          (Former Name or Former Address, if Changed Since Last Report)

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     ITEM 5.     Other Events.

     The Registrant hereby incorporates by reference herein the information set
forth in its Press Release dated May 6, 1999, a copy of which is attached hereto
as Exhibit 99.

     ITEM 7(c).  Exhibits.

     Exhibit 99          Exxon Corporation Press Release dated May 6, 1999
                         announcing Exxon and Mobil expectation of antitrust
                         reviews completion.



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                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.



                                     EXXON CORPORATION


Dated: May 6, 1999                   By: /s/ Donald D. Humphreys
                                         -----------------------
                                          Name:  Donald D. Humphreys
                                          Title: Vice President, Controller and
                                                 Principal Accounting Officer



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                                INDEX TO EXHIBITS




Exhibit No.                                  Description
- ---------------                   ---------------------------------

Exhibit 99             Exxon Corporation Press Release dated May 6, 1999
                       announcing Exxon and Mobil expectation of antitrust
                       reviews completion


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                                                                  Exhibit 99


                                                       FOR IMMEDIATE RELEASE
                                                       THURSDAY, MAY 6, 1999



                EXXON AND MOBIL ANNOUNCE EXPECTATION OF ANTITRUST
                               REVIEWS COMPLETION


         IRVING, TX, and FAIRFAX, VA, May 6 -- Exxon Corporation and Mobil
Corporation announced their expectation that the antitrust reviews of their
proposed merger will be completed by about the end of the third quarter. The
companies filed the formal pre-merger notification with the European Commission
on May 3, 1999. Under the EC's regulatory framework, that process should be
completed around the end of the third quarter. As a result of discussions with
the Federal Trade Commission, the companies believe that the FTC process can be
completed in the same time period.



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For further information, contact:

Exxon Media Relations                                Mobil Media Relations
Phone:  972-444-1107                                 Phone:  703-846-2500