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)      September 24, 1996

                              EXXON CORPORATION                         
            (Exact name of registrant as specified in charter)

New Jersey                          1-2256                    13-5409005
(State or other                  (Commission               (IRS Employer
jurisdiction of incorpo          file number)        Identification No.)

5959 Las Colinas Boulevard, Irving, Texas                     75039-2298
(Address of principal executive offices)                      (Zip Code)

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

Item 5:  Other Events

On September 24, 1996, the United States District Court for the District 
of Alaska entered a judgment in the amount $5,057,571,930 in the Exxon 
Valdez civil trial that began in May 1994.  The District Court awarded 
approximately $19.6 million in compensatory damages, $38 million in 
prejudgment interest on the compensatory damages and $5 billion in 
punitive damages, and ordered that these awards shall bear interest from 
and after entry of the judgment.  On September 27, 1996, the 
District Court stayed execution on the judgment pending appeal, 
contingent on the posting of a $6.75 billion letter of credit which the 
corporation is arranging.  Exxon will appeal the judgment.  The 
corporation continues to believe that the punitive damages in this case 
are unwarranted and that the judgment should be set aside or 
substantially reduced by the appellate courts.

The ultimate cost to the corporation from the lawsuits arising from the 
Exxon Valdez grounding is not possible to predict and may not be 
resolved for a number of years.  For additional information regarding 
these lawsuits see note 3 to the consolidated financial statements 
included in the corporation's Quarterly Report on Form 10-Q for the 
quarter ended June 30, 1996.


    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

                                       /s/        W. Bruce Cook
                               W. Bruce Cook, Vice President, Controller
                               and Principal Accounting Officer

Date: September 27, 1996