1
                       [BAKER & BOTTS, L.L.P. LETTERHEAD]


                                                                     EXHIBIT 8.1
001349.0169                                                                    
                                                                  April 15, 1999



Conoco Inc.
600 North Dairy Ashford
Houston, Texas 77079

Gentlemen:

                  As set forth in the final prospectus supplement dated April
15, 1999 (the "Prospectus Supplement"), which includes a prospectus dated March
24, 1999 that is a part of the Registration Statement on Form S-3 (Registration
No. 333-72291), as amended, filed by Conoco Inc., a Delaware corporation (the
"Company"), with the Securities and Exchange Commission (the "Commission") under
the Securities Act of 1933, as amended (the "Securities Act"), relating to the
proposed public offering (the "Offering") by the Company of $1,350,000,000
principal amount of 5.90% Notes due 2004, $750,000,000 principal amount of 6.35%
Notes due 2009 and $1,900,000,000 principal amount of 6.95% Notes due 2029
(collectively, the "Notes"), certain legal matters in connection with the
Offering are being passed upon for you by us. At your request, this opinion of
counsel is being furnished to you for filing as Exhibit 8.1 to a current report
of the Company on Form 8-K (the "Form 8-K").

                  The statements of legal conclusion that appear in the
Prospectus Supplement under the caption "United States Taxation of Non-United
States Persons" are, subject to the assumptions, qualifications and limitations
set forth therein, our opinion.

                  Pursuant to the provisions of Rule 436(a) of the rules and
regulations of the Commission under the Securities Act, we hereby consent to the
inclusion as aforesaid of our opinion of counsel under the caption "United
States Taxation of Non-United States Persons" in the Prospectus Supplement, to
the references to our Firm under such caption and the caption "Legal Matters" in
the Prospectus Supplement and to the filing of this opinion with the Commission
as an exhibit to the Form 8-K. In giving such consent, we do not admit that we
are within the category of persons whose consent is required under Section 7 of
the Securities Act or the rules and regulations of the Commission thereunder.

                                                          Very truly yours,

                                                          BAKER & BOTTS, L.L.P.