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 to  be filed with the
Securities and  Exchange  Commission  with  respect to  common  stock  of  Exxon
Corporation   offered  or  sold  pursuant  to  Exxon  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>
              LEE R. RAYMOND                Chairman of the Board (Principal Executive        June 28, 1995
 .........................................    Officer)
             (LEE R. RAYMOND)
 
              R. W. BROMERY                 Director                                          June 28, 1995
 .........................................
             (R. W. BROMERY)
 
            D. WAYNE CALLOWAY               Director                                          June 28, 1995
 .........................................
           (D. WAYNE CALLOWAY)
 
                 JESS HAY                   Director                                          June 28, 1995
 .........................................
                (JESS HAY)
 
            JAMES R. HOUGHTON               Director                                          June 28, 1995
 .........................................
           (JAMES R. HOUGHTON)
 
            WILLIAM R. HOWELL               Director                                          June 28, 1995
 .........................................
           (WILLIAM R. HOWELL)
 
           PHILIP E. LIPPINCOTT             Director                                          June 28, 1995
 .........................................
          (PHILIP E. LIPPINCOTT)
 
          MARILYN CARLSON NELSON            Director                                          June 28, 1995
 .........................................
         (MARILYN CARLSON NELSON)
 
               C. R. SITTER                 Director                                          June 28, 1995
 .........................................
              (C. R. SITTER)
 
              JOHN H. STEELE                Director                                          June 28, 1995
 .........................................
             (JOHN H. STEELE)
 
            ROBERT E. WILHELM               Director                                          June 28, 1995
 .........................................
           (ROBERT E. WILHELM)
</TABLE>
 
<TABLE>
<CAPTION>
                SIGNATURE                                      TITLE                              DATE
- ------------------------------------------  --------------------------------------------   -------------------
<S>                                         <C>                                            <C>    
            JOSEPH D. WILLIAMS              Director                                          June 28, 1995
 .........................................
           (JOSEPH D. WILLIAMS)
 
            EDGAR A. ROBINSON               Treasurer (Principal Financial Officer)           June 28, 1995
 .........................................
           (EDGAR A. ROBINSON)
 
                W. B. COOK                  Controller (Principal Accounting Officer)         June 28, 1995
 .........................................
               (W. B. COOK)
</TABLE>