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                               OCEAN ENERGY, INC.,
                              a Texas corporation,

                             successor by merger to
                               OCEAN ENERGY, INC.

                             a Delaware corporation,
                                   as Issuer,

                               OCEAN ENERGY, INC.,
                            a Louisiana corporation,
                            as Subsidiary Guarantor,

                                       and

                  NORWEST BANK MINNESOTA, NATIONAL ASSOCIATION,

                                   as Trustee

                              --------------------

                          FIRST Supplemental Indenture

                           Dated as of March 30, 1999

                                       to

                                    Indenture

                            Dated as of July 8, 1998

                              --------------------



                          7 5/8% Senior Notes due 2005

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<PAGE>

                          FIRST SUPPLEMENTAL INDENTURE

         FIRST SUPPLEMENTAL INDENTURE (this "SUPPLEMENTAL INDENTURE"),  dated as
of March 30, 1999, by and among Ocean  Energy,  Inc., a Texas  corporation  (the
"COMPANY"), as successor by merger to Ocean Energy, Inc., a Delaware corporation
("OLD OEI"),  Ocean  Energy,  Inc.,  a Louisiana  corporation  and  wholly-owned
subsidiary of the Company ("OEI-SUB"), as subsidiary guarantor, and Norwest Bank
Minnesota, National Association, as trustee (the "TRUSTEE").

                                    RECITALS

         WHEREAS, Old OEI, as issuer, OEI-Sub, as subsidiary guarantor,  and the
Trustee are  parties to that  certain  Indenture,  dated as of July 8, 1998 (the
"INDENTURE"),  providing  for the issuance of an aggregate  principal  amount of
$125,000,000 of 7-5/8% Senior Notes due 2005; and

         WHEREAS,  pursuant to the terms of that certain  Agreement  and Plan of
Merger,  dated as of November 24, 1998,  as amended by Amendment  No. 1 thereto,
dated as of  December 9, 1998 (as so amended,  the "MERGER  AGREEMENT"),  by and
between Old OEI and the Company (formerly known as Seagull Energy  Corporation),
Old OEI has merged (the "MERGER") with and into the Company, with the Company as
the surviving entity,  and the Company has changed its name from "Seagull Energy
Corporation" to "Ocean Energy, Inc."; and

         WHEREAS,  pursuant to the Merger Agreement, the Company has assumed all
of the  obligations  of Old OEI under the  Indenture,  as required under Section
5.01 thereof; and

         WHEREAS, pursuant to Section 9.01(b) of the Indenture, the Company, the
Subsidiary  Guarantors  and the Trustee may enter into one or more  supplemental
indentures  without the consent of any Holders to provide for the  assumption of
the obligations of Old OEI under the Indenture by a Successor upon the merger of
Old OEI.

         NOW THEREFORE, in consideration of the foregoing and for other good and
valuable  consideration,  the  receipt  and  sufficiency  of  which  are  hereby
acknowledged,  the Company,  OEI-Sub and the Trustee mutually covenant and agree
for the equal and ratable benefit of the Holders as follows:

         1. Definitions.  Capitalized terms used herein without definition shall
have the meanings  assigned to them in the  Indenture.  For all purposes of this
Supplemental Indenture,  except as otherwise herein expressly provided or unless
the context otherwise  requires,  the words "herein,"  "hereof" and "hereby" and
other words of similar import used in this Supplemental  Indenture refer to this
Supplemental Indenture as a whole and not to any particular section hereof.

         2. Assumption by the Company.  The Company hereby (i) expressly assumes
all the  obligations  of Old OEI under the  Indenture  and the  Notes,  and (ii)
becomes  substituted  for,  and may  exercise  every right and power of, Old OEI
under the Indenture with the same effect as if the Company had  originally  been
named as the issuer of the Notes under the Indenture.

         3. Change of Corporate  Name.  Any and all  references in the Indenture
and Notes to OCEAN ENERGY, INC., a Delaware corporation, or the "Company," shall
be deemed henceforth to refer to OCEAN ENERGY, INC., a Texas corporation.

<PAGE>

         4. Governing  Law. THE INTERNAL LAWS OF THE STATE OF NEW YORK,  WITHOUT
REGARD TO  CONFLICT  OF LAWS  PRINCIPLES  THEREOF,  SHALL  GOVERN AND BE USED TO

CONSTRUE THIS SUPPLEMENTAL INDENTURE.

         5. Trustee Makes No Representation. The Trustee makes no representation
as to the validity or sufficiency of this Supplemental Indenture.

         6.  Counterparts.  The  parties  may sign any  number of copies of this
Supplemental  Indenture.  Each signed copy shall be an original, but all of them
together represent the same agreement.

         7. Effect of Headings.  The Section headings herein are for convenience
of reference  only,  are not to be  considered a part hereof and shall in no way
modify or restrict any of the terms or provisions hereof.

         IN WITNESS  WHEREOF,  the parties hereto have caused this  Supplemental
Indenture to be duly executed as of the date first above written.

                              OCEAN ENERGY, INC., a Texas corporation

                              By: 
                              Name:
                              Title:

                              NORWEST BANK MINNESOTA, NATIONAL ASSOCIATION, 

                              as Trustee

                              By: 
                              Name:
                              Title:

                              SUBSIDIARY GUARANTOR:

                              OCEAN ENERGY, INC., a Louisiana corporation

                              By: 
                              Name:
                              Title: