EXHIBIT 24
 
                               EXXON CORPORATION
                               POWER OF ATTORNEY
 
     Each  person whose signature  appears below constitutes  and appoints T. P.
Townsend, Edgar A. Robinson and  W. B. Cook, and each  of them, his or her  true
and  lawful attorneys-in-fact  and agents, with  full power  of substitution and
resubstitution, for him or her and in his  or her own name, place and stead,  in
any  and all capacities to sign a Registration Statement on form S-3 to be filed
with the Securities  and Exchange Commission  with respect to  Shares of  common
stock of Exxon Corporation offered and sold in connection with the corporation's
Shareholder Investment Program and to sign any and all amendments or supplements
(including  post-effective amendments)  to such  Registration Statement,  and to
file the same,  with all  exhibits thereto,  and other  documents in  connection
therewith,  with  the Securities  and  Exchange Commission,  granting  unto said
attorneys-in-fact and agents, and each of  them, full power and authority to  do
and  perform each and every act and thing requisite and necessary to be done, as
fully to all  intents and purposes  as he or  she might or  could do in  person,
hereby  ratifying and confirming  all that said  attorneys-in-fact and agents or
any of them, or their or his  or her substitute or substitutes, may lawfully  do
or cause be done by virtue hereof.
 
<TABLE>
<CAPTION>
                SIGNATURE                                      TITLE                              DATE
- ------------------------------------------  --------------------------------------------   -------------------
 
<C>                                         <S>                                            <C>
                    *                       Chairman of the Board (Principal Executive        February 20, 1997
 .........................................    Officer)
             (LEE R. RAYMOND)
 
                    *                       Director                                          February 20, 1997
 .........................................
           (MICHAEL J. BOSKIN)
 
                    *                       Director                                          February 20, 1997
 .........................................
           (D. WAYNE CALLOWAY)
 
                    *                       Director                                          February 20, 1997
 .........................................
                (JESS HAY)
 
                    *                       Director                                          February 20, 1997
 .........................................
           (JAMES R. HOUGHTON)
 
                    *                       Director                                          February 20, 1997
 .........................................
           (WILLIAM R. HOWELL)
 
                    *                       Director                                          February 20, 1997
 .........................................
          (PHILIP E. LIPPINCOTT)
 
                    *                       Director                                          February 20, 1997
 .........................................
           (HARRY J. LONGWELL)
 
                    *                       Director                                          February 20, 1997
 .........................................
         (MARILYN CARLSON NELSON)
 
                    *                       Director                                          February 20, 1997
 .........................................
           (ROBERT E. WILHELM)
</TABLE>
 


<TABLE>
<CAPTION>
                SIGNATURE                                      TITLE                              DATE
- ------------------------------------------  --------------------------------------------   -------------------
<C>                                    <S>                                               <C>
 
            EDGAR A. ROBINSON               Treasurer (Principal Financial Officer)         February 20, 1997
 .........................................
           (EDGAR A. ROBINSON)
 
                    *                       Controller (Principal Accounting Officer)       February 20, 1997
 .........................................
               (W. B. COOK)

      *By     /s/ EDGAR A. ROBINSON
 .........................................
           (EDGAR A. ROBINSON)
             ATTORNEY-IN-FACT 
</TABLE>