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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
                      U.S. BANK TRUST NATIONAL ASSOCIATION,

                                   as Trustee

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

                          FIRST Supplemental Indenture

                           Dated as of March 30, 1999

                                       to

                                    Indenture

                            Dated as of July 8, 1998

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



                    8 3/8% Senior Subordinated Notes due 2008

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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 U.S. Bank
Trust 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
$250,000,000 of 8-3/8% Senior Subordinated Notes due 2008; 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 8.1
thereof; and

         WHEREAS, pursuant to Section 8.1(v) of the Indenture,  OEI-Sub is, upon
the  occurrence  of the  Merger,  required to execute a  supplemental  indenture
confirming  that its Subsidiary  Guarantee shall apply to the obligations of the
Company under the Indenture and the Securities; and

         WHEREAS,  pursuant to Section 9.1(a) 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  evidence  the  succession  of
another  Person to the Old OEI and the  assumption by any such  successor of the
covenants of Old OEI contained in the Indenture and in the Securities.

         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 for the due and punctual payment of the principal
of (and premium,  if any, on) and interest on the Securities and the performance
and observance of every covenant

<PAGE>

of the  Indenture on the part of Old OEI, to be performed or observed,  and (ii)
succeeds to, and 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 Securities under the Indenture.

         3.  Confirmation  of Guarantee  by OEI-Sub.  OEI-Sub  hereby  expressly
confirms that, after  consummation of the Merger,  its Subsidiary  Guarantee set
forth in Article XIII of the Indenture and in a notation to the Securities shall
apply to the  obligations  of the  Company  set forth in the  Indenture  and the
Securities. Such Subsidiary Guarantee includes, without limitation, (i) the full
and prompt performance of the Company's  obligations under the Indenture and the
Securities, and (ii) the prompt payment in full of the principal of (premium, if
any,  on) and  interest on the  Securities  when due,  whether at  maturity,  by
acceleration,  redemption or otherwise, and interest on the overdue principal of
and  interest on the  Securities,  if any, to the extent  lawful,  and all other
obligations  of the Company to the Holders or the Trustee under the Indenture or
under the Securities,  all in accordance with the terms of the Indenture and the
Securities.

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

         5. Ratification of Indenture; Supplemental Indenture Part of Indenture.
Except as expressly  amended hereby,  the Indenture is in all respects  ratified
and confirmed and all the terms,  conditions and provisions thereof shall remain
in full force and effect.  This Supplemental  Indenture shall form a part of the
Indenture  for all  purposes,  and every  Holder  of  Securities  heretofore  or
hereafter authenticated and delivered under the Indenture shall be bound hereby.

         6. Governing Law. THIS SUPPLEMENTAL  INDENTURE SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE  WITH THE LAWS OF THE STATE OF NEW YORK,  WITHOUT REGARD

TO PRINCIPLES OF CONFLICTS OF LAWS.

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

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

         9. Effect of Headings.  The Section headings herein are for convenience
only and shall not affect the construction thereof.

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         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:

                               U.S. BANK TRUST NATIONAL ASSOCIATION, as Trustee

                               By:
                               Name:
                               Title:

                               SUBSIDIARY GUARANTOR:

                               OCEAN ENERGY, INC., a Louisiana corporation

                               By:
                               Name:
                               Title: