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                                                                      EXHIBIT 24

                                POWER OF ATTORNEY


         KNOW ALL PERSONS BY THESE PRESENTS, that the person whose signature
appears below appoints each of (1) Michael A. Gist, the Corporate Secretary of
Conoco Inc., a Delaware corporation (the "Company"), (2) Robert W. Goldman, the
Senior Vice President, Finance of the Company and (3) W. David Welch, the
Principal Accounting Officer of the Company, and each of them, severally, as
such person's true and lawful attorney or attorneys-in-fact and agent or agents,
each of whom shall be authorized to act with or without the other, with full
power of substitution and resubstitution, for such person and in such person's
name, place and stead, in any and all capacities, to execute and file, or cause
to be filed, with the Securities and Exchange Commission, any and all amendments
to the Company's Annual Report on Form 10-K for the year ended December 31,
1998, and all materials required by the Securities Exchange Act of 1934, as
amended, with full power and authority to each of said attorneys-in-fact and
agents to do and perform in the name and on behalf of such person, each and
every act and thing whatsoever that is necessary, appropriate or advisable in
connection with any or all the above-described matters and to all intents and
purposes as such person 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.



   /s/ ARCHIE W. DUNHAM                             February 23, 1999
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       Archie W. Dunham                             Date


   /s/ ROBERT W. GOLDMAN                            February 23, 1999
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       Robert W. Goldman                            Date


   /s/ EDGAR S. WOOLARD, JR.                        February 23, 1999
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       Edgar S. Woolard, Jr.                        Date


   /s/  RUTH R. HARKIN                              February 23, 1999
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        Ruth R. Harkin                              Date


   /s/ FRANK A. MCPHERSON                           February 23, 1999
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       Frank A. McPherson                           Date


   /s/  GARY M. PFEIFFER                            February 23, 1999
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        Gary M. Pfeiffer                            Date


   /s/  WILLIAM K. REILLY                           February 23, 1999
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        William K. Reilly                           Date


   /s/  WILLIAM R. RHODES                           February 23, 1999
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        William R. Rhodes                           Date


   /s/  FRANKLIN A. THOMAS                          February 23, 1999
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        Franklin A. Thomas                          Date