<PAGE>   1
 
                                                                      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 his 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, 1996 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>
<CAPTION>
                      SIGNATURE                                      TITLE                         DATE
                      ---------                                      -----                         ----
<C>                                                    <S>                                 <C>
 
                /s/ ROBERT L. KEISER                   Chairman of the Board, Chief           March 6, 1997
-----------------------------------------------------    Executive Officer, President,
                 (Robert L. Keiser)                      and Director (principal
                                                         executive officer)
 
                  /s/ JERRY W. BOX                     Executive Vice President, Chief        March 6, 1997
-----------------------------------------------------    Operating Officer, and Director
                   (Jerry W. Box)
 
              /s/ EDWARD W. MONEYPENNY                 Executive Vice President, Finance,     March 6, 1997
-----------------------------------------------------    Chief Financial Officer, and
               (Edward W. Moneypenny)                    Director (principal financial
                                                         officer)
 
               /s/ ROBERT L. THOMPSON                  Comptroller and Corporate Planning     March 6, 1997
-----------------------------------------------------    Director (principal accounting
                (Robert L. Thompson)                     officer)
 
               /s/ WILLIAM E. BRADFORD                 Director                               March 6, 1997
-----------------------------------------------------
                (William E. Bradford)
 
                 /s/ SYLVIA A. EARLE                   Director                               March 6, 1997
-----------------------------------------------------
                  (Sylvia A. Earle)
 
            /s/ DAVID C. GENEVER-WATLING               Director                               March 6, 1997
-----------------------------------------------------
             (David C. Genever-Watling)
 
                 /s/ ROBERT B. GILL                    Director                               March 6, 1997
-----------------------------------------------------
                  (Robert B. Gill)
 
             /s/ DAVID S. HOLLINGSWORTH                Director                               March 6, 1997
-----------------------------------------------------
              (David S. Hollingsworth)
 
             /s/ CHARLES H. PISTOR, JR.                Director                               March 6, 1997
-----------------------------------------------------
              (Charles H. Pistor, Jr.)
 
                 /s/ PAUL R. SEEGERS                   Director                               March 6, 1997
-----------------------------------------------------
                  (Paul R. Seegers)
 
              /s/ IAN L. WHITE-THOMSON                 Director                               March 6, 1997
-----------------------------------------------------
               (Ian L. White-Thomson)
</TABLE>