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                               OCEAN ENERGY, INC.,
                              a Texas corporation,

                                    as Issuer

                                       and
                              THE BANK OF NEW YORK,

                                   as Trustee

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

                          FIRST Supplemental Indenture

                           Dated as of March 30, 1999

                                       to

                                SENIOR Indenture

                            Dated as of July 15, 1993

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



                           7 7/8% Senior Notes due 2003

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<PAGE>

7

                          FIRST SUPPLEMENTAL INDENTURE

         FIRST SUPPLEMENTAL INDENTURE (this "SUPPLEMENTAL INDENTURE"),  dated as
of March 30, 1999, by and among Ocean Energy,  Inc.  (formerly  known as Seagull
Energy Corporation),  a Texas corporation (the "ISSUER"),  Ocean Energy, Inc., a
Louisiana  corporation ("OEI SUB"), and The Bank of New York, a New York banking
association, as trustee (the "TRUSTEE").

                                    RECITALS

         WHEREAS,  the Issuer and the Trustee are parties to that certain Senior
Indenture,  dated as of July 15, 1993 (the  "Indenture"),  pursuant to which the
Issuer has issued an aggregate  principal amount of $100,000,000 of 77/8% Senior
Notes due 2003; 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,  by and between  Ocean  Energy,  Inc.,  a Delaware
corporation  ("OLD OCEAN"),  and the Issuer,  Old Ocean has merged with and into
the Issuer,  with the Issuer as the surviving entity, and the Issuer has changed
its name to "Ocean Energy, Inc., a Texas corporation"; and

         WHEREAS, OEI Sub is a wholly owned subsidiary of the Issuer; and

         WHEREAS,  pursuant to Section 8.1(c) of the Indenture, the Issuer, when
authorized by a resolution of its Board of Directors,  and the Trustee may enter
into one or more supplemental  indentures  without the consent of the Holders to
add to the covenants of the Issuer under the Indenture  such further  covenants,
restrictions,  conditions  or  provisions  as the Issuer and the  Trustee  shall
consider  to be for  the  protection  of the  Holders  of all or any  series  of
Securities; and

         WHEREAS,  the Issuer desires and has requested the Trustee to join with
it and OEI Sub in entering into this  Supplemental  Indenture for the purpose of
amending and  supplementing  the  Indenture in certain  respects as permitted by
Section 8.1(c).

         NOW THEREFORE, in consideration of the foregoing and for other good and
valuable consideration, the receipt of which is hereby acknowledged, the Issuer,
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. Change of Corporate  Name. Any and all references in the Indenture to Seagull
Energy  Corporation or the "Issuer" shall be deemed henceforth to refer to Ocean
Energy, Inc., a Texas corporation.
<PAGE>

3. Designation of Restricted  Subsidiaries.  The Issuer's Board of Directors has
designated the Subsidiaries listed in the resolutions attached hereto as Exhibit
A to be  "Restricted  Subsidiaries"  under  the  Indenture.  The  Issuer  hereby
delivers to the  Trustee the  certified  resolutions  of the Board of  Directors
giving effect to such designations, which are attached hereto as Exhibit A.

4.       Amendments.

                  (a)      Article One.  Article One of the Indenture is hereby 
amended to add the following terms and their respective definitions in proper 
alphabetical order:

         "Adjusted Net Assets" of a Subsidiary  Guarantor at any date shall mean
the  amount  by  which  the fair  value of the  properties  and  assets  of such
Subsidiary Guarantor exceeds the total amount of liabilities, including, without
limitation,  contingent  liabilities (after giving effect to all other fixed and
contingent  liabilities  incurred  or  assumed  on  such  date),  but  excluding
liabilities under the Subsidiary Guarantee, of such Subsidiary Guarantor at such
date.

         "Subsidiary  Guarantee"  means any  guarantee of the  Securities by any
Subsidiary Guarantor pursuant to Article Thirteen hereof.

         "Subsidiary   Guarantor"   means  each  of  the   Issuer's   Restricted
Subsidiaries,  if any,  that becomes a guarantor of the  Securities  pursuant to
Section  13.1  hereof  and  executes  a  supplemental  indenture  in which  such
Restricted  Subsidiary  agrees to be bound by the terms of this  Indenture  as a
Subsidiary  Guarantor,  in each case until such time as the Subsidiary Guarantee
of such Person is released in accordance with the provisions of Article Thirteen
hereof.

                  (b)  Section  8.1.  Section  8.1 of the  Indenture  is  hereby
amended as follows:

                           (i)      by deleting the word "and" at the end of 

paragraph (e);

                           (ii) by deleting the "." at the end of paragraph  (f)

and inserting "; and" in place thereof; and

(iii)    by adding a new paragraph (g) as follows:

                                    "(g)  to   reflect   the   release   of  any
                           Subsidiary  Guarantor from its Subsidiary  Guarantee,
                           or the addition of any  Restricted  Subsidiary of the
                           Issuer  as a  Subsidiary  Guarantor,  in  the  manner
                           provided in this Indenture."

                  (c) Article Thirteen. The following is hereby added as Article
Thirteen of the Indenture:

<PAGE>

                                ARTICLE THIRTEEN

                                   GUARANTEES

         SECTION 13.1      Subsidiary Guarantees.

         The Issuer may designate any  Restricted  Subsidiary to be a Subsidiary
Guarantor.  Any such designation shall be evidenced by a certified resolution of
the Board of Directors delivered to the Trustee. Subject to Section 13.5 hereof,
each  Subsidiary  Guarantor  hereby,  jointly  and  severally,   unconditionally
guarantees  to each  Holder of a Security  authenticated  and  delivered  by the
Trustee and to the Trustee and its  successors  and assigns,  the Securities and
the obligations of the Issuer hereunder and thereunder, that:

                  (a) the  principal  of,  premium,  if any, and interest on the
Securities  will be promptly  paid in full when due,  subject to any  applicable
grace period, whether at maturity, by acceleration, redemption or otherwise, and
interest on the overdue principal,  premium,  if any (to the extent permitted by
law),  and interest on any interest,  if any, on the  Securities,  and all other
payment  obligations  of the Issuer to the Holders or the Trustee  hereunder  or
thereunder  will be promptly paid in full and performed,  all in accordance with
the terms hereof and thereof; and

                  (b) in case of any  extension of time of payment or renewal of
any Securities or any of such other obligations,  the same will be promptly paid
in full when due or performed in  accordance  with the terms of the extension or
renewal,  subject to any applicable grace period, whether at stated maturity, by
acceleration, redemption or otherwise.

         Failing  payment  when  so due  of  any  amount  so  guaranteed  or any
performance so guaranteed for whatever reason, the Subsidiary Guarantors will be
jointly and severally obligated to pay the same immediately. An Event of Default
under this  Indenture or the  Securities  shall  constitute  an event of default
under the Subsidiary Guarantees, and shall entitle the Holders to accelerate the
obligations of the Subsidiary Guarantors hereunder in the same manner and to the
same extent as the obligations of the Issuer.  The Subsidiary  Guarantors  agree
that their  obligations  hereunder shall be  unconditional,  irrespective of the
validity or enforceability  of the Securities or this Indenture,  the absence of
any action to enforce the same, any waiver or consent by any Holder with respect
to any provisions  hereof or thereof,  the recovery of any judgment  against the
Issuer,  any action to enforce  the same or any other  circumstance  which might
otherwise  constitute a legal or equitable  discharge or defense of a Subsidiary
Guarantor.  Each Subsidiary Guarantor waives diligence,  presentment,  demand of
payment,  notice of  acceleration,  notice of  intent to  accelerate,  filing of
claims with a court in the event of insolvency or bankruptcy of the Issuer,  any
right to require a proceeding first against the Issuer,  protest, notice and all
demands  whatsoever.  If any Holder or the  Trustee is  required by any court or
otherwise to return to the Issuer, the Subsidiary Guarantors,  or any liquidator
or other  similar  official  acting  in  relation  to either  the  Issuer or the
Subsidiary Guarantors, any amount paid by the Issuer or any Subsidiary Guarantor
to the  Trustee  or  such  Holder,  the  Subsidiary  Guarantee,  to  the  extent
theretofore  discharged by such  payment,  shall be reinstated in full force and
effect.  Each Subsidiary  Guarantor agrees that it shall not be entitled to, and
waives,  any right to  exercise  any right of  subrogation  in  relation  to the
Holders in respect of any obligations guaranteed by the

<PAGE>

Subsidiary  Guarantee,  except as  provided  under  Section  13.5  hereof.  Each
Subsidiary Guarantor further agrees that, as between the Subsidiary  Guarantors,
on the one hand,  and the Holders and the  Trustee,  on the other hand,  (x) the
maturity  of the  obligations  guaranteed  by the  Subsidiary  Guarantee  may be
accelerated  as provided in Article 5 hereof for the purposes of its  Subsidiary
Guarantee,  notwithstanding any stay, injunction or other prohibition preventing
such acceleration in respect of the obligations  guaranteed thereby,  and (y) in
the event of any declaration of acceleration of such  obligations as provided in
Article  5 hereof,  such  obligations  (whether  or not due and  payable)  shall
forthwith become due and payable by each Subsidiary Guarantor for the purpose of
its Subsidiary Guarantee. The Subsidiary Guarantors shall have the right to seek
contribution from any non-paying  Subsidiary  Guarantor pursuant to Section 13.5
after the Securities and the obligations  hereunder shall have been paid in full
to the Holders under the Subsidiary Guarantees.

         SECTION 13.2      Execution and Delivery of Subsidiary Guarantee.

         To evidence its Subsidiary  Guarantee set forth in Section 13.1 hereof,
each Subsidiary  Guarantor  shall execute and deliver a supplemental  indenture,
which  supplemental  indenture  shall be executed  on behalf of such  Subsidiary
Guarantor,  by manual or facsimile  signature,  by an officer of such Subsidiary
Guarantor.

         Each  Subsidiary  Guarantor  agrees that its  Subsidiary  Guarantee set
forth  in  Section   13.1  hereof   shall   remain  in  full  force  and  effect
notwithstanding  any failure to endorse on each Security  (whether issued before
or after the date such Subsidiary  Guarantor  becomes a Subsidiary  Guarantor) a
notation of such Subsidiary Guarantee.

         SECTION 13.3      Subsidiary Guarantors May Consolidate, Etc., on 
Certain Terms.

         No Subsidiary  Guarantor may consolidate or merge with or into (whether
or not such Subsidiary  Guarantor is the surviving Person) another Person unless
the Person  formed by or surviving  any such  consolidation  or merger (if other
than such  Subsidiary  Guarantor,  another  Subsidiary  Guarantor or the Issuer)
assumes  all  the  obligations  of  such  Subsidiary  Guarantor  pursuant  to  a
supplemental  indenture, in a form reasonably satisfactory to the Trustee, under
the  Securities and this  Indenture.  In the case of any such  consolidation  or
merger  and  upon  the  assumption  by the  successor  Person,  by  supplemental
indenture  executed and delivered to the Trustee,  of the Subsidiary  Guarantee,
such  successor  Person shall succeed to and be  substituted  for the Subsidiary
Guarantor  with the same effect as if it had been named  herein as a  Subsidiary
Guarantor.

         SECTION 13.4      Releases of Subsidiary Guarantees.

         The Issuer may designate any Subsidiary Guarantor, at any time and from
time to time,  to be released from its  Subsidiary  Guarantee if (i) no Event of
Default has occurred and is continuing,  and (ii) such  designation  and release
will not cause the occurrence of an Event of Default. Any such designation shall
be evidenced by a certified  resolution  of the Board of Directors  delivered to
the Trustee.  Upon delivery of such  certified  resolution to the Trustee,  such
Subsidiary Guarantor shall be automatically and immediately released from all of
its obligations

<PAGE>

under its Subsidiary Guarantee,  this Indenture and the Securities. If requested
by the  Issuer,  the  Trustee  will join  with the  Issuer  and such  Subsidiary
Guarantor in executing and  delivering a supplemental  indenture  evidencing the
release  of such  Subsidiary  Guarantor  from all of its  obligations  under its
Subsidiary Guarantee, this Indenture and the Securities.

        SECTION 13.5 Limitation on Subsidiary Guarantor Liability; Contribution.

         Each Subsidiary  Guarantor,  and by its acceptance  hereof each Holder,
hereby  confirms that it is the intention of all such parties that the guarantee
by such Subsidiary Guarantor pursuant to its Subsidiary Guarantee not constitute
a  fraudulent  transfer or  fraudulent  conveyance  for purposes of any federal,
state or foreign law. To  effectuate  the foregoing  intention,  the Holders and
each Subsidiary  Guarantor hereby irrevocably agree that the obligations of each
Subsidiary  Guarantor  under its  Subsidiary  Guarantee  shall be limited to the
maximum  amount as will,  after giving effect to all other  contingent and fixed
liabilities  of  such  Subsidiary  Guarantor  and  after  giving  effect  to any
collections  from or  payments  made by or on  behalf  of any  other  Subsidiary
Guarantor in respect of the obligations of such other Subsidiary Guarantor under
its  Subsidiary  Guarantee  or  pursuant  to this  Section  13.5,  result in the
obligations of such  Subsidiary  Guarantor  under its  Subsidiary  Guarantee not
constituting a fraudulent conveyance or fraudulent transfer under federal, state
or foreign law.  This  Section 13.5 is for the benefit of the  creditors of each
Subsidiary Guarantor.

         In order to  provide  for just and  equitable  contribution  among  the
Subsidiary  Guarantors,  the Subsidiary  Guarantors agree, inter se, that in the
event  any  payment  or  distribution  is made by any  Subsidiary  Guarantor  (a
"Funding  Guarantor")  under its Subsidiary  Guarantee,  such Funding  Guarantor
shall be entitled to a  contribution  from each other  Subsidiary  Guarantor (if
any) in a pro rata amount based on the  Adjusted  Net Assets of each  Subsidiary
Guarantor  (including  the  Funding  Guarantor)  for all  payments,  damages and
expenses  incurred  by  that  Funding  Guarantor  in  discharging  the  Issuer's
obligations with respect to the Securities or any other  Subsidiary  Guarantor's
obligations with respect to its Subsidiary Guarantee.

5.  Designation  of Subsidiary  Guarantor.  The Issuer's  Board of Directors has
designated OEI Sub to be a Subsidiary Guarantor under the Indenture.  The Issuer
hereby  delivers  to the  Trustee  the  certified  resolution  of the  Board  of
Directors giving effect to such designation, which is attached hereto as Exhibit
A. OEI Sub hereby agrees to be a Subsidiary  Guarantor under the Indenture,  and
agrees to  guarantee  the  Securities  and be bound by the other  covenants  and
obligations  of a  Subsidiary  Guarantor,  all to the  extent  set  forth in the
Indenture, as modified by this Supplemental Indenture.

6. Ratification of Indenture;  Supplemental Indentures 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 shall be bound hereby.

7. Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY AND CONSTRUED
IN  ACCORDANCE  WITH  THE LAWS OF THE 

<PAGE>

STATE OF NEW YORK, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS.

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

9. 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.

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

                            [Signature Page Follows]

<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:

                                      Stephen A. Thorington,
                                      Senior Vice President - Finance,
                                      Treasury & Corporate Development

                                  THE BANK OF NEW YORK, as Trustee

                                    By:
                                    Name:
                                    Title:

                                  OCEAN ENERGY, INC., a Louisiana corporation

                                    By: 

                                        James C. Flores, President