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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

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                          THIRD Supplemental Indenture

                           Dated as of March 30, 1999

                                       to

                                    Indenture

                          Dated as of October 30, 1995

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



                   10 3/8% Senior Subordinated Notes due 2005

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<PAGE>

                          THIRD SUPPLEMENTAL INDENTURE

         THIRD 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,  formerly known as First Trust of New York, National
Association, as trustee (the "TRUSTEE").

                                    RECITALS

         WHEREAS,   Old  OEI,  as  successor   by  merger  to  United   Meridian
Corporation, a Delaware corporation ("UMC"), as issuer, OEI-Sub, as successor by
merger to UMC Petroleum  Corporation,  a Delaware  corporation  ("UMC-SUB"),  as
subsidiary  guarantor,  and the Trustee are parties to that  certain  Indenture,
dated  as of  October  30,  1995,  as  supplemented  by the  First  Supplemental
Indenture,  dated as of November 4, 1997,  among UMC, UMC-Sub and First Trust of
New York, National Association,  successor to Bank of Montreal Trust Company, as
Trustee, and the Second Supplemental  Indenture,  dated as of March 27, 1998, by
and  among  Old  OEI,  OEI-Sub,  and  the  Trustee  (as  so  supplemented,   the
"INDENTURE"),  providing  for the issuance of an aggregate  principal  amount of
$150,000,000 of 10.375% Senior Subordinated 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 OEI under the  Indenture,  as required under Section 8.1
thereof; and

         WHEREAS, pursuant to Section 8.1(e) 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 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,  

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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 of the covenants and other  obligations  of Old OEI under the Securities and
the  Indenture,  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 principal of 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 the prompt  payment in full and
performance  of 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  obligations  of the Company  thereunder and under the
Securities shall remain in full force and effect.  This  Supplemental  Indenture
shall form a part of the Indenture for all purposes, and every Holder 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.

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

<PAGE>

         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: