<PAGE>   1
                                                                     EXHIBIT 4.1

                      SECOND AMENDMENT TO RIGHTS AGREEMENT

         This Second Amendment to the Rights Agreement between Conoco Inc.
(formerly known as Conoco Energy Company), a Delaware corporation (the
"Company"), and First Chicago Trust Company of New York, a New York corporation
(the "Rights Agent"), dated October 19, 1998, as amended October 20, 1998 (the
"Rights Agreement"), is hereby adopted as of July 29, 1999.

         WHEREAS, the Company's Class A Common Stock and Class B Common Stock
may be held either in certificated form or through book-entry accounts at the
offices of the Company's transfer agent; and

         WHEREAS, the Rights Agreement currently provides only for certificated
Common Stock.

         NOW, THEREFORE, pursuant to Section 26 of the Rights Agreement, the
Rights Agreement is hereby amended as follows:

1. Section 3 of the Rights Agreement is hereby amended to read in its entirety
as follows:

         "Section 3. Issuance of Rights Certificates.

                           (a) Until the earlier of (i) the close of business on
         the tenth Business Day after the Stock Acquisition Date (or, if the
         tenth Business Day after the Stock Acquisition Date occurs before the
         Record Date, the close of business on the Record Date), or (ii) the
         close of business on the tenth Business Day (or such later date as the
         Board shall determine) after the date that a tender or exchange offer
         by any Person (other than the Company, any Subsidiary of the Company,
         any employee benefit plan of the Company or of any Subsidiary of the
         Company, or any Person or entity organized, appointed or established by
         the Company for or pursuant to the terms of any such plan) is first
         published or sent or given within the meaning of Rule 14d-2(a) of the
         General Rules and Regulations under the Exchange Act, if upon
         consummation thereof, such Person would become an Acquiring Person (the
         earlier of (i) and (ii) being herein referred to as the "Distribution
         Date"), (x) the Class A Rights and the Class B Rights, respectively,
         will be evidenced (subject to the provisions of paragraph (b) of this
         Section 3) by the certificates for the Class A Common Stock and the
         Class B Common Stock, respectively, registered in the names of the
         holders of such class of Common Stock (which certificates for such
         class of Common Stock shall be deemed also to be certificates for such
         Rights) or, for Common Stock registered in the names of the holders
         thereof and held in book-entry accounts at the offices of the Company's
         transfer agent, by such book-entry accounts, and not by separate Rights
         Certificates, and (y) the Rights will be transferable only in
         connection with the transfer of the underlying shares of Common Stock
         (including transfers to the Company). As soon as practicable after the
         Distribution Date, the Rights Agent will send by first-class,
         postage-prepaid mail, to each record holder of Class A Common Stock and
         Class B Common Stock,






                                       1

<PAGE>   2


         respectively, as of the close of business on the Distribution Date, at
         the address of such holder shown on the records of the Company, one or
         more right certificates, in substantially the form of Exhibit B and C
         hereto, evidencing one Class A Right for each share of Class A Common
         Stock (a "Class A Rights Certificate") and one Class B Right for each
         share of Class B Common Stock (a "Class B Rights Certificate"),
         respectively, so held, subject to adjustment as provided herein. In the
         event that any adjustment in the number of Rights per share of Common
         Stock has been made pursuant to Section 11(p) hereof, at the time of
         distribution of the Rights Certificates, the Company shall make the
         necessary and appropriate rounding adjustments (in accordance with
         Section 14(a) hereof) so that Rights Certificates representing only
         whole numbers of Rights are distributed and cash is paid in lieu of any
         fractional Rights. As of and after the Distribution Date, the Rights
         will be evidenced solely by such Rights Certificates.

               (b) The Company will make available, as promptly as practicable
         following the Record Date, a copy of a Summary of Rights, in
         substantially the form attached hereto as Exhibit C (the "Summary of
         Rights") to any holder of Rights who may so request from time to time
         prior to the Expiration Date. With respect to the Class A Common Stock
         and the Class B Common Stock, respectively, outstanding as of the
         Record Date, or issued subsequent to the Record Date, unless and until
         the Distribution Date shall occur, the Class A Rights and the Class B
         Rights will be evidenced by certificates for such class of Common Stock
         or by the book-entry accounts at the offices of the Company's transfer
         agent, and the registered holders of the Common Stock shall also be the
         registered holders of the associated Rights. Until the earlier of the
         Distribution Date or the Expiration Date (as such term is defined in
         Section 7(a) hereof), the transfer of any shares of Common Stock in
         respect of which Rights have been issued shall also constitute the
         transfer of the Rights associated with such shares of Common Stock.

               (c) Rights shall be issued in respect of all shares of Common
         Stock which are issued (whether originally issued or from the Company's
         treasury) after the Record Date but prior to the earlier of the
         Distribution Date or the Expiration Date (including an issuance of
         Class A Common Stock upon the conversion, whether automatic or
         voluntary, of Class B Common Stock into Class A Common Stock (and for
         purposes of the foregoing, any deemed conversion of Class B Common
         Stock upon the transfer of such shares or otherwise shall be deemed to
         be an issuance of Class A Common Stock)). Certificates representing
         such shares of Class A Common Stock shall also be deemed to be
         certificates for the associated Class A Rights, and shall bear the
         following legend:

               This certificate also evidences and entitles the holder hereof to
               certain Class A Rights as set forth in the Rights Agreement
               between Conoco Inc. (the "Company") and First Chicago Trust
               Company of New York (the "Rights Agent") dated as of October 19,
               1998 (the "Rights Agreement"), the terms of which are hereby
               incorporated herein by reference and a copy of which is on file
               at the principal offices of the




                                       2


<PAGE>   3


               Company. Under certain circumstances, as set forth in the Rights
               Agreement, such Class A Rights will be evidenced by separate
               certificates and will no longer be evidenced by this certificate.
               The Company will mail to the holder of this certificate a copy of
               the Rights Agreement, as in effect on the date of mailing,
               without charge, promptly after receipt of a written request
               therefor. Under certain circumstances set forth in the Rights
               Agreement, Class A Rights issued to, or held by, any Person who
               is, was or becomes an Acquiring Person or any Affiliate or
               Associate thereof (as such terms are defined in the Rights
               Agreement), whether currently held by or on behalf of such Person
               or by any subsequent holder, may become null and void.

Certificates representing such shares of Class B Common Stock shall also be
deemed to be certificates for the associated Class B Rights, and shall bear the
following legend:

               This certificate also evidences and entitles the holder hereof to
               certain Class B Rights as set forth in the Rights Agreement
               between Conoco Inc. (the "Company") and First Chicago Trust
               Company of New York (the "Rights Agent") dated as of October 19,
               1998, as amended (the "Rights Agreement"), the terms of which are
               hereby incorporated herein by reference and a copy of which is on
               file at the principal offices of the Company. Under certain
               circumstances, as set forth in the Rights Agreement, such Class B
               Rights will be evidenced by separate certificates and will no
               longer be evidenced by this certificate. The Company will mail to
               the holder of this certificate a copy of the Rights Agreement, as
               in effect on the date of mailing, without charge, promptly after
               receipt of a written request therefor. Under certain
               circumstances set forth in the Rights Agreement, Class B Rights
               issued to, or held by, any Person who is, was or becomes an
               Acquiring Person or any Affiliate or Associate thereof (as such
               terms are defined in the Rights Agreement), whether currently
               held by or on behalf of such Person or by any subsequent holder,
               may become null and void.

A book-entry account for shares of Class A Common Stock shall also be deemed to
include the associated Class A Rights, and the stock distribution statement for
such shares shall bear the following legend:

               Each share of Class A Common Stock entitles the holder to certain
               Class A Rights as set forth in a Rights Agreement between Conoco
               Inc. (the "Company") and First Chicago Trust Company of New York,
               dated as of October 19, 1998, as amended (the "Rights
               Agreement"), the terms of which are hereby incorporated herein by
               reference and a copy of which is on file at the principal offices
               of the Company. Under certain circumstances, as set forth in the
               Rights Agreement, such Class A Rights will be evidenced by
               separate certificates and will no longer be associated with
               shares of Class A Common Stock. The Company will mail to any
               beneficial holder of shares of Class A Common Stock a copy



                                       3


<PAGE>   4
               of the Rights Agreement, as in effect on the date of mailing,
               without charge, promptly after receipt of a written request
               therefor. Under certain circumstances set forth in the Rights
               Agreement, Class A Rights issued to any Person who is, was or
               becomes an Acquiring Person or an Affiliate or Associate thereof
               (as such terms are defined in the Rights Agreement), whether
               currently held by or on behalf of such Person or by any
               subsequent holder, may become null and void.

A book-entry account for shares of Class B Common Stock shall also be deemed to
include the associated Class B Rights, and the stock distribution statement for
such shares shall bear the following legend:

               Each share of Class B Common Stock entitles the holder to certain
               Class B Rights as set forth in a Rights Agreement between Conoco
               Inc. (the "Company") and First Chicago Trust Company of New York,
               dated as of October 19, 1998, as amended (the "Rights
               Agreement"), the terms of which are hereby incorporated herein by
               reference and a copy of which is on file at the principal offices
               of the Company. Under certain circumstances, as set forth in the
               Rights Agreement, such Class B Rights will be evidenced by
               separate certificates and will no longer be associated with
               shares of Class B Common Stock. The Company will mail to any
               beneficial holder of shares of Class B Common Stock a copy of the
               Rights Agreement, as in effect on the date of mailing, without
               charge, promptly after receipt of a written request therefor.
               Under certain circumstances set forth in the Rights Agreement,
               Class B Rights issued to any Person who is, was or becomes an
               Acquiring Person or an Affiliate or Associate thereof (as such
               terms are defined in the Rights Agreement), whether currently
               held by or on behalf of such Person or by any subsequent holder,
               may become null and void.

Until the earlier of (i) the Distribution Date or (ii) the Expiration Date, the
Rights associated with the Common Stock represented by such certificates or held
in such book-entry accounts shall be evidenced by such certificates or such
book-entry accounts alone and registered holders of Common Stock shall also be
the registered holders of the associated Rights, and the transfer of any shares
of Common Stock, whether by transfer of physical certificates or book-entry
transfer, shall also constitute the transfer of the Rights associated with the
Common Stock."

2. Section 12 is hereby amended to read in its entirety as follows:

                           "Section 12. Certificate of Adjusted Purchase Price
         or Number of Shares. Whenever an adjustment is made as provided in
         Section 11 and Section 13 hereof, the Company shall (a) promptly
         prepare a certificate setting forth such adjustment and a brief
         statement of the facts accounting for such adjustment, (b) promptly
         file with the Rights Agent, and with each transfer agent for the
         Preferred Stock and the Common Stock, a copy of such certificate and
         (c) if a Distribution Date has occurred, mail a brief summary thereof
         to each holder of a Rights Certificate (or, if prior to the
         Distribution Date, to each registered holder of shares






                                       4


<PAGE>   5


         of Common Stock). The Rights Agent shall be fully protected in relying
         on any such certificate and on any adjustment therein contained."

3. Section 16, paragraph (c) is hereby amended to read in its entirety as
follows:

                           (c) subject to Section 6(a) and Section 7(f) hereof,
         the Company and the Rights Agent may deem and treat the person in whose
         name a Rights Certificate is registered (or, prior to the Distribution
         Date, the person in whose name the associated Common Stock certificate
         is registered or the person listed as a registered holder of shares of
         Common Stock through a book-entry account at the offices of the
         Company's transfer agent) as the absolute owner thereof and of the
         Rights evidenced thereby (notwithstanding any notations of ownership or
         writing on the Rights Certificates or the associated Common Stock
         certificate made by anyone other than the Company or the Rights Agent)
         for all purposes whatsoever, and neither the Company nor the Rights
         Agent, subject to the last sentence of Section 7(e) hereof, shall be
         required to be affected by any notice to the contrary; and"

4. Section 18, paragraph (b) is hereby amended to read in its entirety as
follows:

                           "(b) The Rights Agent shall be protected and shall
         incur no liability for or in respect of any action taken, suffered or
         omitted by it in connection with its administration of this Agreement
         in reliance upon any Rights Certificate or certificate for Common Stock
         or for other securities of the Company or book-entry account records of
         the Company's transfer agent, instrument of assignment or transfer,
         power of attorney, endorsement, affidavit, letter, notice, direction,
         consent, certificate, statement, or other paper or document believed by
         it to be genuine and to be signed, executed and, where necessary,
         verified or acknowledged, by the proper Person or Persons."

5. Section 25 is hereby amended to read in its entirety as follows:

                           "Section 25. Notices. Notices or demands authorized
         by this Agreement to be given or made by the Rights Agent or by the
         holder of any Rights Certificate to or on the Company shall be
         sufficiently given or made if sent by first-class mail, postage
         prepaid, addressed (until another address is filed in writing by the
         Rights Agent with the Company) as follows:

                  Conoco Inc.
                  600 North Dairy Ashford
                  Houston, Texas 77079
                  Attention: Corporate Secretary

         Subject to the provisions of Section 21, any notice or demand
         authorized by this Agreement to be given or made by the Company or by
         the holder of any Rights Certificate to or on the Rights Agent shall be
         sufficiently given or made if sent by first-




                                       5


<PAGE>   6
         class mail, postage prepaid, addressed (until another address is filed
         in writing by the Rights Agent with the Company) as follows:

                  First Chicago Trust Company of New York
                  525 Washington Blvd., Suite 4660
                  Jersey City, NJ 07310
                  Attention: Tenders and Exchanges Administration

         Notices or demands authorized by this Agreement to be given or made by
         the Company or the Rights Agent to the holder of any Rights Certificate
         (or, if prior to the Distribution Date, to the registered holder of
         shares of Common Stock) shall be sufficiently given or made if sent by
         first-class mail, postage prepaid, addressed to such holder at the
         address of such holder as shown on the registry books of the Company."

6. The first sentence of Section 26 is hereby amended to read as follows:

         "Prior to the Distribution Date, the Company and the Rights Agent
         shall, if the Company so directs, supplement or amend any provision of
         this Agreement without the approval of any registered holders of shares
         of Common Stock."

7. This Second Amendment to the Rights Agreement may be executed in any number
of counterparts and each of such counterparts shall for all purposes be deemed
to be an original, and all such counterparts shall together constitute but one
and the same instrument.

                  IN WITNESS WHEREOF, the parties hereto have caused this Second
Amendment to the Rights Agreement to be duly executed as of the date first above
written.


CONOCO INC.                              FIRST CHICAGO TRUST COMPANY OF NEW YORK


By: /s/ RICK A. HARRINGTON               By: /s/ JOHN F. KEEGAN
   -----------------------------------   --------------------------------------
Name:   Rick A. Harrington               Name:   John F. Keegan
Title:  Senior Vice President, Legal,    Title:  Assistant Vice President
          and General Counsel

Consented to effective as of the date first above written:


E.  I.  DU PONT DE NEMOURS AND
COMPANY


By: /s/ GARY M. PFEIFFER
   ------------------------------------
Name:   Gary M. Pfeiffer
Title:  Senior Vice President, Finance,
          and Chief Financial Officer

                                       6