<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 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, 1997 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
<S>                                       <C>                                               <C>
         /S/ ROBERT L. KEISER              Chairman of the Board, Chief
---------------------------------------    Executive Officer, and                            March 5, 1998  
          (Robert L. Keiser)               Director (principal executive officer)                             
                                           

           /s/ JERRY W. BOX                President, Chief Operating
---------------------------------------    Officer and Director                              March 5, 1998
            (Jerry W. Box)                 

       /s/ EDWARD W. MONEYPENNY            Executive Vice President,
---------------------------------------    Finance, Chief Financial                          March 5, 1998
        (Edward W. Moneypenny)             Officer, and Director (principal                                 
                                           financial officer)                                               
                                           

        /s/ ROBERT L. THOMPSON             Vice President Planning and 
---------------------------------------    Controller (principal                             March 5, 1998
         (Robert L. Thompson)              accounting officer)
                                           

        /s/ WILLIAM E. BRADFORD            Director                                          March 5, 1998
---------------------------------------
         (William E. Bradford)

          /S/ SYLVIA A. EARLE              Director                                          March 5, 1998
---------------------------------------
           (Sylvia A. Earle)

     /S/ DAVID C. GENEVER-WATLING          Director                                          March 5, 1998
---------------------------------------
      (David C. Genever-Watling)
</TABLE>


<PAGE>   2



<TABLE>
<S>                                       <C>                                               <C>
         /s/ ROBERT B. GILL               Director                                          March 5, 1998
---------------------------------------
          (Robert B. Gill)

                                          Director                                          March 5, 1998
---------------------------------------
      (David S. Hollingsworth)

     /s/ CHARLES H. PISTOR, JR.           Director                                          March 5, 1998
---------------------------------------
      (Charles H. Pistor, Jr.)

         /s/ PAUL R. SEEGERS              Director                                          March 5, 1998
---------------------------------------
          (Paul R. Seegers)

      /s/ IAN L. WHITE-THOMSON            Director                                          March 5, 1998
---------------------------------------
       (Ian L. White-Thomson)
</TABLE>