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                                                                     EXHIBIT 1.2



                                   CONOCO INC.
                                   ("COMPANY")

                                 DEBT SECURITIES


                                 TERMS AGREEMENT



                                                                 October 3, 2001


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 October 3, 2001 ("UNDERWRITING AGREEMENT"), the
following securities ("OFFERED SECURITIES") on the following terms:

         TITLE:       Floating Rate Notes Due October 15, 2002 ("2002 NOTES").
                      Floating Rate Notes Due April 15, 2003 ("2003 NOTES").

         PRINCIPAL AMOUNT:  $500,000,000 of 2002 Notes
                            $500,000,000 of 2003 Notes

         INTEREST: Floating rate, subject to adjustment on a quarterly basis,
     based on the three-month LIBOR rate plus 0.77% on the 2002 Notes, and
     floating rate, subject to adjustment on a quarterly basis based on the
     three-month LIBOR rate plus 0.85%, in each case from October 11, 2001,
     payable on January 15, April 15, July 15 and October 15 of each year,
     commencing January 15, 2002.

         MATURITY:  October 15, 2002 for the 2002 Notes
                    April 15, 2003 for the 2003 Notes

         SINKING FUND:  None.

         LISTING:  Luxembourg Stock Exchange.

         PURCHASE PRICE: 99.85% of principal amount of the 2002 Notes; and
     99.80% of principal amount of the 2003 Notes.



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         EXPECTED REOFFERING PRICE: 100.00% of principal amount of the 2002
     Notes; and 100.00% of principal amount of the 2003 Notes.

         CLOSING: 10:00 A.M. on October 11, 2001, 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:

                  Banc of America Securities LLC
                  9 West 57th Street
                  New York, NY 10019

                  Deutsche Bank Alex. Brown Inc.
                  31 West 52nd Street
                  New York, NY 10019

                  J.P. Morgan Securities Inc.
                  270 Park Avenue
                  New York, NY  10017

         The principal amount of the Offered Securities to be purchased by each
of the Underwriters is 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), Conoco Limited, Conoco (U.K.) Limited and Conoco
Canada Resources Limited.

         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 Regulations 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; (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; and
(iv) will comply with all applicable securities laws and


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regulations in force in any jurisdiction in which it purchases, offers, sells or
delivers Offered Securities or possesses or distributes the Prospectus.

         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 first two sentences appearing in the third
paragraph under the caption "Underwriting" in the prospectus supplement and the
information contained in the paragraphs regarding the United Kingdom in the
fourth paragraph, the sentence regarding market making in the next paragraph and
the eighth and ninth paragraphs 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/ Rick A. Harrington
                                               --------------------------------
                                               Name:  Rick A. Harrington
                                               Title: Senior Vice President,
                                                      Legal, and General Counsel


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


         Banc of America Securities LLC,
         Deutsche Bank Alex. Brown Inc.,
         J.P. Morgan Securities Inc.,

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

         By  J.P. Morgan Securities Inc.


         By      /s/ Steve Christensen
            -----------------------------
              Name:  Steve Christensen
              Title: Vice President


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                                   SCHEDULE A

<Table>
<Caption>
                                            PRINCIPAL          PRINCIPAL
                                            AMOUNT OF          AMOUNT OF
              UNDERWRITER                   2002 NOTES         2003 NOTES
              -----------                   ----------         ----------
                                                        
Banc of America Securities LLC..........  $ 155,000,000       $ 155,000,000
Deutsche Banc Alex. Brown Inc...........    155,000,000         155,000,000
J.P. Morgan Securities Inc. ............    155,000,000         155,000,000
The Royal Bank of Scotland plc..........     25,000,000          25,000,000
Bayerische Hypo- und Vereinsbank AG.....     10,000,000          10,000,000

         Total..........................  $ 500,000,000       $ 500,000,000
                                          =============       =============
</Table>