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                                                                     EXHIBIT 1.2



                                   CONOCO INC.
                                   ("COMPANY")

                                 DEBT SECURITIES


                                 TERMS AGREEMENT



                                                                  April 15, 1999


To:  The Representatives of the Underwriters identified herein



Dear Sirs:

         The undersigned agrees to sell to the several Underwriters named in
Schedule A hereto for their respective accounts, on and subject to the terms and
conditions of the Underwriting Agreement to be filed by the Company in its
Report on Form 8-K dated April 16, 1999 ("UNDERWRITING AGREEMENT"), the
following securities ("OFFERED SECURITIES") on the following terms:

         TITLE:       5.90% Notes due 2004 ("2004 NOTES").
                      6.35% Notes due 2009 ("2009 NOTES").
                      6.95% Notes due 2029 ("2029 NOTES").

                  PRINCIPAL AMOUNT: $1,350,000,000 of 2004 Notes, $750,000,000
         of 2009 Notes, and $1,900,000,000 of 2029 Notes.

                  INTEREST: 5.90% per annum on the 2004 Notes, 6.35% per annum
         on the 2009 Notes, and 6.95% per annum on the 2029 Notes, in each case
         from April 20, 1999, payable semiannually on April 15 and October 15,
         commencing October 15, 1999, to holders of record on the preceding
         April 1 or October 1, as the case may be.

                  MATURITY: April 15, 2004 for the 2004 Notes.
                            April 15, 2009 for the 2009 Notes.
                            April 15, 2029 for the 2029 Notes.


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                  OPTIONAL REDEMPTION: The Company may redeem the Offered
         Securities of each series, in whole or in part, at any time and from
         time to time, according to the price formula set forth in the
         Prospectus Supplement.

                  SINKING FUND: None.

                  LISTING: Luxembourg Stock Exchange.

                  PURCHASE PRICE: 99.356% of principal amount for the 2004
         Notes; 99.350% of principal amount for the 2009 Notes; and 99.125% of
         principal amount for the 2029 Notes plus, in each case, accrued
         interest, if any, from April 20, 1999.

                  EXPECTED REOFFERING PRICE: 99.856% of principal amount for the
         2004 Notes; 100.000% of principal amount for the 2009 Notes; and
         100.000% of principal amount for the 2029 Notes, in each case subject
         to change by the Representatives.

                  CLOSING: 10:00 A.M. on April 20, 1999, at the offices of
         Cravath, Swaine & Moore, 825 Eighth Avenue, New York, New York 10019 in
         Federal (same day) funds.

                  SETTLEMENT AND TRADING: Book-Entry Only via DTC.

                  BLACKOUT: Until 14 days after the Closing Date.

                  NAMES AND ADDRESSES OF REPRESENTATIVES:

                         Credit Suisse First Boston Corporation
                         11 Madison Avenue
                         New York, NY  10010-3629

                         Attention:  Investment Banking Department,
                                     Transaction Advisory Group

                         Salomon Smith Barney Inc.
                         388 Greenwich Street, 34th Floor
                         New York, NY 10013

         The respective principal amounts of the Offered Securities to be
purchased by each of the Underwriters are set forth opposite their names in
Schedule A hereto.

         The provisions of the Underwriting Agreement are incorporated herein by
reference. The Material Subsidiaries of the Company are Conoco Inc. (formerly
Continental Oil Company), Norske Conoco A/S, Conoco Mineraloel GmbH, Conoco
Limited, Conoco (U.K.) Limited, Conoco Oil & Gas Associates L.P., Conoco Asia
Limited, Lobo Pipeline Company and Conoco Development Ltd. The Company and its




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affiliates own, directly or indirectly, a total of approximately 74% of the
partnership interests in Conoco Oil & Gas Associates L.P.

         The Offered Securities will be made available for checking and
packaging at the offices of Cravath, Swaine & Moore at least 24 hours prior to
the Closing Date.

         Each Underwriter severally represents and agrees that (i) it has not
offered or sold, and prior to the date six months after the date of issue of the
Offered Securities will not offer or sell, any Offered Securities to persons in
the United Kingdom except to persons whose ordinary activities involve them in
acquiring, holding, managing or disposing of investments (as principal or agent)
for the purpose of their businesses or otherwise in circumstances which have not
resulted and will not result in an offer to the public in the United Kingdom
within the meaning of the Public Offers of Securities Reglations 1995; (ii) it
has complied and will comply with all applicable provisions of the Financial
Services Act 1986 with respect to anything done by it in relation to the Offered
Securities in, from or otherwise involving the United Kingdom; and (iii) it has
only issued or passed on and will only issue or pass on in the United Kingdom
any document received by it in connection with the issue of the Offered
Securities to a person who is of a kind described in Article 11(3) of the
Financial Services Act 1986 (Investment Advertisements) (Exemptions) Order 1996
or is a person to whom such document may otherwise lawfully be issued or passed
on.

         The Underwriters agree that they will reimburse the Company $1,650,000
for certain of the Company's expenses in connection with the offering of the
Offered Securities.

         For purposes of Section 6 of the Underwriting Agreement, the only
information furnished to the Company by any Underwriter for use in the
Prospectus consists of the following information in the Prospectus furnished on
behalf of each Underwriter: the concession and reallowance figures appearing in
the paragraph under the caption "Underwriting" in the prospectus supplement and
the information contained in the paragraphs regarding the United Kingdom, the
sentence regarding market making in the next paragraph and the penultimate
paragraph under the caption "Underwriting" in the prospectus supplement.

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                  If the foregoing is in accordance with your understanding of
         our agreement, kindly sign and return to the Company one of the
         counterparts hereof, whereupon it will become a binding agreement
         between the Company and the several Underwriters in accordance with its
         terms.

                              Very truly yours,

                                   Conoco Inc.

                                   By /s/ M. W. Espinosa 
                                     ---------------------------------
                                     M. W. Espinosa          
                                     Treasurer


The foregoing Terms Agreement is hereby 
confirmed and accepted as of the date
first above written.

         Credit Suisse First Boston Corporation,
         Salomon Smith Barney Inc.,

         Acting on behalf of themselves and as the 
         Representatives of the several Underwriters.

         By  Credit Suisse First Boston Corporation


         By /s/ Wallace C. Henderson
            ---------------------------------------
            Name: Wallace C. Henderson
            Title: Managing Director

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                                   SCHEDULE A





                                                                       PRINCIPAL            PRINCIPAL         PRINCIPAL
                                                                       AMOUNT OF            AMOUNT OF         AMOUNT OF
                         UNDERWRITER                                   2004 NOTES           2009 NOTES        2029 NOTES
                         -----------                                   ----------           ----------        ----------

                                                                                                              
Credit Suisse First Boston Corporation........................       $  465,750,000        $258,750,000     $  655,500,000
Salomon Smith Barney Inc. ....................................          465,750,000         258,750,000        655,500,000
Chase Securities Inc..........................................           67,500,000          37,500,000         95,000,000
Goldman, Sachs & Co...........................................           67,500,000          37,500,000         95,000,000
Lehman Brothers Inc...........................................           67,500,000          37,500,000         95,000,000
Merrill Lynch, Pierce, Fenner & Smith                                                                                      
            Incorporated......................................           67,500,000          37,500,000         95,000,000
Morgan Stanley & Co. Incorporated.............................           67,500,000          37,500,000         95,000,000
NationsBanc Montgomery Securities LLC.........................           67,500,000          37,500,000         95,000,000
The Bank of Tokyo-Mitsubishi, Ltd.............................            1,687,500             937,500          2,375,000
Bayerische Hypo- und Vereinsbank AG...........................            1,687,500             937,500          2,375,000
Blaylock & Partners, L.P......................................            1,687,500             937,500          2,375,000
Commerzbank Capital Markets Corporation.......................            1,687,500             937,500          2,375,000
Credit Lyonnais Securities (USA) Inc..........................            1,687,500             937,500          2,375,000
Greenwich NatWest Ltd. (as agent for National                                                                              
    Westminster Bank, Plc)....................................            1,687,500             937,500          2,375,000
SG Cowen Securities Corporation...............................            1,687,500             937,500          2,375,000
SunTrust Equitable Securities Corporation.....................            1,687,500             937,500          2,375,000
                                                                     --------------        ------------     --------------
         Total................................................       $1,350,000,000        $750,000,000     $1,900,000,000
                                                                     ==============        ============     ==============