1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                    FORM 8-K

                                 CURRENT REPORT

                       Pursuant to Section 13 or 15(d) of
                       the Securities Exchange Act of 1934



        Date of Report (date of earliest event reported): APRIL 15, 1999



                                   CONOCO INC.
             (Exact name of registrant as specified in its charter)




                                                                                    
              DELAWARE                                 1-14521                              51-0370352
    (State or other jurisdiction              (Commission File Number)                   (I.R.S. Employer
          of incorporation)                                                             Identification No.)




      600 NORTH DAIRY ASHFORD ROAD
             HOUSTON, TEXAS                                            77079
(Address of principal executive offices)                            (Zip Code)



       Registrant's telephone number, including area code: (281) 293-1000





   2



ITEM 5.           OTHER EVENTS.

                  On April 15, 1999, Conoco Inc. (the "Company") entered into a
Terms Agreement (incorporating by reference the terms of an Underwriting
Agreement relating to unsecured debt securities (the "Underwriting Agreement"))
dated April 15, 1999 (the "Terms Agreement") with Credit Suisse First Boston
Corporation and Salomon Smith Barney Inc., as representatives of the several
underwriters named in Schedule A to the Terms Agreement, relating to the
offering by the Company of $1,350,000,000 aggregate principal amount of 5.90%
Notes due 2004, $750,000,000 aggregate principal amount of 6.35% Notes due 2009
and $1,900,000,000 aggregate principal amount of 6.95% Notes due 2029
(collectively, the "Notes") under its Registration Statement on Form S-3
(Registration No. 333-72291; the "Registration Statement"). The Notes will be
issued under an Indenture, dated as of April 15, 1999, between the Company and
Bank One, N.A., as trustee (the "Trustee"), a form of which was filed as Exhibit
4.1 to the Registration Statement. Each of the (i) Terms Agreement, (ii) the
form of the Underwriting Agreement, (iii) the terms of the Notes, including the
form of Note, (iv) an opinion of Baker & Botts, L.L.P., counsel to the Company,
as to certain tax matters relating to the Notes and (v) the Statement of
Eligibility and Qualification under the Trust Indenture Act of 1939 of the
Trustee on Form T-1 is being filed as an exhibit to this report.

ITEM 7.           FINANCIAL STATEMENTS AND EXHIBITS

         (c)      Exhibits.

         1.1      --        Form of Underwriting Agreement relating to unsecured
                            debt securities

         1.2      --        Terms Agreement dated April 15, 1999 between the
                            Company and Credit Suisse First Boston Corporation
                            and Salomon Smith Barney Inc., as representatives of
                            the several underwriters named in Schedule A to the
                            Terms Agreement

         4.1      --        Terms of the Notes, including the form of Note

         8.1      --        Opinion of Baker & Botts, L.L.P., counsel to the 
                            Company, as to certain tax matters relating to the
                            Notes

         25.1     --        Statement of Eligibility and Qualification under 
                            the Trust Indenture Act of 1939 of Bank One, N.A. on
                            Form T-1

                                       -2-

   3


                                    SIGNATURE



                  Pursuant to the requirements of the Securities Exchange Act of
1934, the Registrant has duly caused this report to be signed on its behalf by
the undersigned hereunto duly authorized.


                                  CONOCO INC.



                                  By: /s/ Rick A. Harrington
                                     -----------------------------------------
                                     Rick A. Harrington
                                     Senior Vice President, Legal, and 
                                     General Counsel


Date: April 16, 1999

                                       -3-



   4

                                 EXHIBIT INDEX


                                                                   
         1.1      --        Form of Underwriting Agreement relating to unsecured
                            debt securities

         1.2      --        Terms Agreement dated April 15, 1999 between the
                            Company and Credit Suisse First Boston Corporation
                            and Salomon Smith Barney Inc., as representatives of
                            the several underwriters named in Schedule A to the
                            Terms Agreement

         4.1      --        Terms of the Notes, including the form of Note

         8.1      --        Opinion of Baker & Botts, L.L.P., counsel to the 
                            Company, as to certain tax matters relating to the
                            Notes

         25.1     --        Statement of Eligibility and Qualification under 
                            the Trust Indenture Act of 1939 of Bank One, N.A. on
                            Form T-1