EXHIBIT 5

                      AMENDMENT NO. 2 TO RIGHTS AGREEMENT
                      -----------------------------------


         Amendment  No.  2,  dated  as of  September  30,  1996,  to the  Rights
Agreement,  dated as of December 16, 1988, between Burlington  Resources Inc., a
Delaware corporation (the "Company"), and The First National Bank of Boston (the
"Rights  Agent"),  as amended by Amendment  No. 1, dated as of February 23, 1989
(as amended, the "Rights Agreement").

         The Company and the Rights Agent  desire to amend the Rights  Agreement
pursuant to Section 27 thereof.

         Accordingly, the parties hereto agree as follows:

     1. Definitions. Each capitalized term defined in the Rights Agreement shall
have the same meaning in this Amendment No. 2 as in the Rights Agreement, unless
otherwise provided herein.

     2.  Amendment.  Section 1(a) of the Rights  Agreement is hereby  amended by
deleting  such  definition  in its  entirety  and adding the  following  in lieu
thereof:

     ""Acquiring  Person"  shall mean any  Person  (as such term is  hereinafter
defined),  who  or  which,  together  with  all  Affiliates  (as  such  term  is
hereinafter  defined) and Associates  (as such term is  hereinafter  defined) of
such Person,  without the prior approval of the Company, shall be the Beneficial
Owner (as such term is hereinafter  defined) of securities  representing  15% or
more of the Voting Power (as such term is hereinafter defined) or who was such a
Beneficial  Owner at any time after the date hereof,  whether or not such Person
continues to be the Beneficial  Owner of securities  representing 15% or more of
the Voting Power, but shall not include (i) the Company,  (ii) any subsidiary of
the Company (as such term is hereinafter  defined),  (iii) any employee  benefit
plan of the  Company  or any of its  subsidiaries  or (iv)  any  entity  holding
securities of the Company organized,  appointed or established by the Company or
any  of its  subsidiaries  for  or  pursuant  to the  terms  of any  such  plan.
Notwithstanding  the  foregoing,  no Person shall be deemed to be an  "Acquiring
Person"  either  (i) as a result of the  subsequently  reported  acquisition  of
securities  with Voting  Power by the Company  which,  by reducing the number of
securities with Voting Power outstanding,  increases the proportional  number of
securities with Voting Power beneficially owned by such Person together with all
Affiliates  and  Associates of such Person;  provided that if (a) a Person would
become an Acquiring  Person (but for the operation of this  subclause  (i)) as a
result of the  acquisition of securities  with Voting Power by the Company,  and
(b) after  such  securities acquisition  by the  Company,  such  Person,  or an
Affiliate  or  Associate  of such  Person,  at a time  when  such  Person is the
Beneficial  Owner of  securities  representing  15% or more of the Voting Power,
becomes the  Beneficial  Owner of any  additional  securities  with Voting Power
(other  than a  pro-rata  distribution),  then  such  Person  shall be deemed an
Acquiring  Person,  or (ii)if the Board of Directors  of the Company  determines
that a Person who would otherwise be an "Acquiring  Person," as defined pursuant




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to the  foregoing  provisions  of this  paragraph  has in good faith become such
inadvertently  and such Person  either (a) divests as promptly as  practicable a
sufficient  number of securities  with Voting Power so that such Person would no
longer be an "Acquiring Person" as defined pursuant to the foregoing  provisions
of this  paragraph  or (b)  acquired  the  securities  without any  intention of
changing or  influencing  control of the  Company,  and  reports its  Beneficial
Ownership of securities  with Voting Power on Schedule 13(g) under Rule 13d-1 or
13d-2 of the Exchange  Act and such  Person,  or an Affiliate or an Associate of
such Person,  does not, after such Board  determination  and at a time when such
Person is the  Beneficial  Owner of securities  representing  15% or more of the
Voting Power,  become the  Beneficial  Owner of any additional  securities  with
Voting Power,  then such Person shall not be deemed to be an "Acquiring  Person"
for any purpose of this Agreement."

     3. Rights Agreement.  Except as amended hereby,  the Rights Agreement shall
remain in full force and effect.

     4.  Governing  Law.  This  Amendment No. 2 shall be deemed to be a contract
made  under  the laws of the State of  Delaware  and for all  purposes  shall be
governed and construed in accordance  with the laws of such state  applicable to
contracts to be made and to be performed entirely within such state.

     5.  Counterparts.  This  Amendment  No. 2 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.

     6. Descriptive  Headings.  Descriptive Headings of this Amendment No. 2 are
inserted  for  convenience  only and shall not  control or affect the meaning or
construction of any of the provisions hereof.

     IN WITNESS WHEREOF,  the parties hereto have caused this Amendment No. 2 to
be duly executed and their respective corporate seals to be hereunto affixed and
attested, all as of the day and year first above written.

ATTEST:                                     THE FIRST NATIONAL BANK OF BOSTON

                                            By:  /s/ COLLEEN H. SHEA
- --------------------------                       --------------------------
                                                 Colleen H. Shea
                                                 Administration Manager


ATTEST:                                     BURLINGTON RESOURCES INC.

                                            By:  /s/ GERALD J. SCHISSLER
- ---------------------------                      --------------------------
                                                 Gerald J. Schissler
                                                 Executive Vice President,
                                                  Law and Corporate Affairs




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