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                                                                      EXHIBIT 24
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS:
 
     Each person whose signature appears below constitutes and appoints Jack E.
Little, S.A. Lackey, and Jack B. Edrington, and each of them, his or her true
and lawful attorney-in-fact and agent, with full power of substitution and
resubstitution, for such person and in his or her name, place and stead, in any
and all capacities, to sign the Shell Oil Company Annual Report on Form 10-K for
the fiscal year ended December 31, 1998, and any and all amendments thereto, 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 substitute or substitutes, may lawfully do or cause
to be done by virtue hereof.
 
     IN WITNESS WHEREOF, the undersigned hereto set his or her hand this 4th day
of March, 1999.
 

                                                    
 
               /s/ JOSEPH E. ANTONINI                  /s/ RAND V. ARASKOG
- -----------------------------------------------------  -----------------------------------------------------
            Joseph E. Antonini, Director               Rand V. Araskog, Director
 
                /s/ ROBERT F. DANIELL                  /s/ VILMA S. MARTINEZ
- -----------------------------------------------------  -----------------------------------------------------
             Robert F. Daniell, Director               Vilma S. Martinez, Director
 
                 /s/ STEVE L. MILLER                   /s/ MARK MOODY-STUART
- -----------------------------------------------------  -----------------------------------------------------
              Steve L. Miller, Director                Mark Moody-Stuart, Director
 
                /s/ HAROLD A. POLING                   /s/ GORDON R. SULLIVAN
- -----------------------------------------------------  -----------------------------------------------------
         Harold A. Poling, Emeritus Director           Gordon R. Sullivan, Director
 
/s/ JOHN F. WOODHOUSE
- -----------------------------------------------------
John F. Woodhouse, Director

 
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