<PAGE>
                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
    KNOW  ALL MEN  BY THESE PRESENTS,  that each person  whose signature appears
below constitutes and appoints  Robert L. Keiser and  Edward W. Moneypenny,  and
each of them (with full power to each of them to act alone), his true and lawful
attorney-in-fact  and agent, with full power of substitution and resubstitution,
for him and in his name, place and stead, in any and all capacities to sign  the
Annual Report of Oryx Energy Company for the fiscal year ended December 31, 1995
on  Form 10-K pursuant to Section 13 or  15(d) of the Securities Exchange Act of
1934 and any or all amendments to the  Annual Report 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 in  and  about  the
premises,  as fully  to all  intents and  purposes as  he might  or could  do in
person, hereby  ratifying and  confirming all  that said  attorneys-in-fact  and
agents or any of them, or their substitutes, may lawfully do or cause to be done
by virtue hereof.
 
<TABLE>
<C>                                                     <S>                                   <C>
                      SIGNATURE                                        TITLE                         DATE
------------------------------------------------------  ------------------------------------  -------------------
 
                                                        Chairman of the Board, Chief
                 /s/ ROBERT L. KEISER                    Executive Officer, President, and
     -------------------------------------------         Director (principal executive           March 7, 1996
                  (Robert L. Keiser)                     officer)
                   /s/ JERRY W. BOX
     -------------------------------------------        Executive Vice President, Chief          March 7, 1996
                    (Jerry W. Box)                       Operating Officer and Director
                                                        Executive Vice President, Finance,
               /s/ EDWARD W. MONEYPENNY                  Chief Financial Officer, and
     -------------------------------------------         Director (principal financial           March 7, 1996
                (Edward W. Moneypenny)                   officer)
                /s/ ROBERT L. THOMPSON                  Comptroller and Corporate Planning
     -------------------------------------------         Director (principal accounting          March 7, 1996
                  Robert L. Thompson                     officer)
               /s/ WILLIAM E. BRADFORD
     -------------------------------------------        Director                                 March 7, 1996
                (William E. Bradford)
                  /s/ ROBERT B. GILL
     -------------------------------------------        Director                                 March 7, 1996
                   (Robert B. Gill)
              /s/ DAVID S. HOLLINGSWORTH
     -------------------------------------------        Director                                 March 7, 1996
               (David S. Hollingsworth)
              /s/ CHARLES H. PISTOR, JR.
     -------------------------------------------        Director                                 March 7, 1996
               (Charles H. Pistor, Jr.)
                 /s/ PAUL R. SEEGERS
     -------------------------------------------        Director                                 March 7, 1996
                  (Paul R. Seegers)
               /s/ IAN L. WHITE-THOMSON
     -------------------------------------------        Director                                 March 7, 1996
                (Ian L. White-Thomson)
</TABLE>