SEAGULL ENERGY CORPORATION


                                   RESOLUTIONS
                                     of the
                              CHAIRMAN OF THE BOARD

                             7 1/2% Senior Notes due
                               September 15, 2027


     WHEREAS,  on  September  16,  1997,  the Board of  Directors of the Company
approved the issuance by the Company,  of up to $150,000,000  aggregate  initial
offering  prices of bonds,  debentures,  notes  and/or  other  debt  obligations
(collectively, the "Securities");

     WHEREAS,  the Board of Directors has authorized the Executive  Committee of
the Company or the Chairman of the Board of the Company to  determine  the terms
and conditions of the Securities;

     NOW, THEREFORE, in furtherance of the foregoing,  the Chairman of the Board
of the Company hereby adopts the following resolutions:

RESOLVED,  that pursuant to the authority delegated to the Chairman of the Board
by the Board of Directors  of Seagull  Energy  Corporation  (the  "Company")  by
resolutions adopted on September 16, 1997, a series of Securities referred to in
such resolutions shall be issued and designated under the Senior Indenture dated
as of  September  1, 1997 among the  Company and The Bank of New York as trustee
(the  "Indenture"),  as the Company's 7 1/2% Senior Notes Due September 15, 2027
(the "Senior Notes"); and

     FURTHER  RESOLVED,  that in addition to the terms provided in the Indenture
with  respect to  Securities  of a series  issued  thereunder,  the terms of the
Senior Notes shall be as follows (with all  capitalized  terms used below having
the respective meanings ascribed thereto in the Indenture):

          (1) The  aggregate  principal  amount  of the  Senior  Notes  shall be
     $150,000,000;

          (2) The stated  maturity of the principal of the Senior Notes shall be
     September 15, 2027;

          (3) The Senior  Notes  shall bear  interest  at the rate of 7 1/2% per
     annum from September 30, 1997 or from the most recent interest payment date
     to which  interest has been paid or duly provided for, which interest shall
     be  calculated  on the basis of a 360-day year  comprised of twelve  30-day
     months;


          (4) The interest  payment dates with respect to the Senior Notes shall
     be March 15 and September 15 in each year,  commencing  March 15, 1998, and
     the regular record dates for interest  payable on any such interest payment
     date shall be March 1 or  September 1 (whether or not a Business  Day),  as
     the case may be, next preceding such interest payment date;

          (5)  Principal  of (and  premium,  if any) and  interest on the Senior
     Notes shall be payable at the Corporate  Trust Office of the Trustee in New
     York, New York, and the Senior Notes may be surrendered for registration of
     transfer  or  exchange  at such  Corporate  Trust  Office,  and notices and
     demands to or upon the  Company  in  respect  of the  Senior  Notes and the
     Indenture may be served at such Corporate Trust Office;

          (6) The  Trustee  shall act as  paying  agent,  authenticating  agent,
     transfer agent and security registrar with respect to the Senior Notes;

          (7) The Senior Notes shall not be redeemable prior to stated maturity;

          (8)  The  Senior  Notes  shall  not  be  subject  to  a  sinking  fund
     requirement;

          (9) The Senior Notes shall be issuable in  denominations of $1,000 and
     integral multiples thereof;

          (10) The Senior  Notes shall be subject to  defeasance  as provided in
     Section 10(C) of the Indenture;

          (11) The  Senior  Notes  will be  issued  wholly in the form of Global
     Securities,  and The Depository  Trust Company shall be the Depositary with
     respect thereto; and

          (12) The Senior  Notes  shall be in  substantially  the form  attached
     hereto as Exhibit A;

     FURTHER RESOLVED, that the form of Underwriting Agreement and related Terms
Agreement to be executed with the  underwriters  named below with respect to the
offer and sale of the Senior Notes,  in the form submitted to this meeting,  and
the form of  Prospectus  Supplement  dated  September  25, 1997 to the Company's
Prospectus dated September 19, 1997, are hereby approved;  and the execution and
delivery  on behalf of the  Company  of such  Underwriting  Agreement  and Terms
Agreement by the Chairman of the Board,  the President or any Vice  President of
the Company is ratified and approved; and

     FURTHER RESOLVED,  that Merrill Lynch,  Pierce,  Fenner & Smith,  Donaldson
Lufkin & Jenrette  Securities  Corporation,  J.P. Morgan & Co., Salomon Brothers
Inc and SBC Warburg  Dillon Read Inc. are  selected as the several  underwriters
(the  "Underwriters")  to which the Senior Notes shall be sold; that the sale of
an aggregate of  $150,000,000  of Senior  Notes to such  Underwriters  is hereby
authorized  and approved;  that the purchase  price to be paid to the Company by
the  Underwriters  shall be 98.544% of the principal amount of the Senior Notes;
and that the initial  public  offering  price shall be 99.544% of the  principal
amount of the Senior Notes; and


     FURTHER RESOLVED, that the Chairman of the Board, the President or any Vice
President  of the Company,  or any of them,  are hereby  authorized,  for and on
behalf of the Company,  to execute any  agreements  or take any other actions as
such officer shall in his sole discretion deem necessary or advisable to arrange
for  the  Senior  Notes  to be  included  as  book-entry  only  security  in the
facilities of The Depository Trust Company;

     FURTHER RESOLVED, that the Chairman of the Board, the President or any Vice
President  of the Company,  or any of them,  are hereby  authorized,  for and on
behalf  of the  Company,  to  execute  and  deliver  all  agreements,  powers of
attorney, certificates or other instruments and documents, and to take all other
actions,  as such  officer  shall  in his  sole  discretion  deem  necessary  or
advisable to carry out the transactions approved in the preceding resolutions.

     EXECUTED and effective as of this 25th day of September, 1997.


                                      /s/ Barry J. Galt
                                          Barry J. Galt
                                          Chairman of the Board



     THIS  SECURITY IS A GLOBAL  SECURITY  WITHIN THE  MEANING OF THE  INDENTURE
HEREINAFTER  REFERRED  TO AND IS  REGISTERED  IN THE NAME OF A  DEPOSITORY  OR A
NOMINEE OF A  DEPOSITORY.  UNLESS AND UNTIL IT IS  EXCHANGED IN WHOLE OR IN PART
FOR  SECURITIES  IN  DEFINITIVE  REGISTERED  FORM,  THIS  SECURITY  MAY  NOT  BE
TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITARY TO THE NOMINEE OF THE DEPOSITARY
OR BY A NOMINEE OF THE  DEPOSITARY TO THE  DEPOSITARY OR ANOTHER  NOMINEE OF THE
DEPOSITARY OR BY THE DEPOSITARY OR ANY SUCH NOMINEE TO A SUCCESSOR DEPOSITARY OR
A NOMINEE OF SUCH SUCCESSOR DEPOSITARY.


     Unless this certificate is presented by an authorized representative of The
Depository Trust Company, a New York corporation  ("DTC"), to the Company or its
agent for registration of transfer,  exchange,  or payment,  and any certificate
issued is  registered  in the name of Cede &  Co.  or in such  other  name as is
requested  by an  authorized  representative  of DTC (and any payment is made to
Cede &  Co.  or  to  such  other  entity  as  is  requested  by  an   authorized
representative  of DTC), ANY TRANSFER,  PLEDGE, OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE  BY OR TO ANY PERSON IS  WRONGFUL  inasmuch  as the  registered  owner
hereof, Cede & Co., has an interest herein.


                           SEAGULL ENERGY CORPORATION

                     7 1/2% Senior Notes due September 15, 2027

No. BE-1                                                    CUSIP No. 812007AE2


SEAGULL ENERGY CORPORATION,  a corporation duly organized and existing under the
laws of the State of Texas (herein called the "Company," which term includes any
successor  Person  under  the  Indenture  hereinafter  referred  to),  for value
received,  hereby  promises to pay to Cede & Co.,  or  registered  assigns,  the
principal sum of ONE HUNDRED FIFTY MILLION DOLLARS  ($150,000,000)  on September
15, 2027,  and to pay interest  thereon from September 30, 1997 or from the most
recent  interest  payment date to which  interest has been paid or duly provided
for,  semiannually  in  arrears  on  March  15 and  September  15 in each  year,
commencing March 15, 1998, at the rate of 7 1/2% per annum,  until the principal
hereof  is fully  paid or made  available  for full  payment.  The  interest  so
payable,  and punctually paid or duly provided for, on any interest payment date
will,  as provided in such  Indenture,  be paid to the Person in whose name this
Security is  registered  at the close of business on the March 1 or  September 1
(whether  or not a  Business  Day),  as the case  may be,  next  preceding  such
interest payment date (a "Regular Record Date").  Notwithstanding the foregoing,
if and to the extent the Company  shall  default in the payment of the  interest
due on such interest  payment date, any such interest not so punctually  paid or
duly  provided  for will  forthwith  cease to be  payable  to the Holder on such
Regular  Record Date and such  defaulted  interest  shall instead be paid to the
Person in whose name this Security is registered (a) at the close of business on
a subsequent  record date (which shall be not less than five Business Days prior
to the date of payment of such defaulted interest)


established  by  notice  given by mail by or on  behalf  of the  Company  to the
Holders of Securities  not less than 15 days preceding  such  subsequent  record
date or (b) as determined by such other  procedure as is mutually  acceptable to
the Company and the Trustee, all as more fully described in the Indenture.

     Payment of the  principal  of (and  premium,  if any) and  interest on this
Security shall be made at the Corporate Trust Office of the Trustee in New York,
New York,  or at such other office or agency of the Company as it may  designate
for such  purpose  pursuant to the  Indenture  hereinafter  referred to, in such
immediately  available  funds of the United  States of America as at the time of
payment are legal tender for payment of public and private debts.

     Reference  is hereby made to the further  provisions  of this  Security set
forth below,  which  further  provisions  shall for all  purposes  have the same
effect as if set forth in this place.

     Unless the  certificate of  authentication  hereon has been executed by the
Trustee  referred to below by manual  signature of an authorized  officer,  this
Security shall not be entitled to any benefit under the Indenture or be valid or
obligatory for any purpose.

     IN WITNESS  WHEREOF,  the  Company has caused  this  instrument  to be duly
executed under its corporate seal.

Dated: September 30, 1997

                                            SEAGULL ENERGY CORPORATION


                                            By:_________________________ 
                                               Barry J. Galt
                                               Chairman of the Board and
                                               Chief Executive Officer


ATTEST:


______________________________________
Stephen A. Thorington
Treasurer





                     TRUSTEE'S CERTIFICATE OF AUTHENTICATION


     This is one of the Securities of the series  designated  herein referred to
in the within-mentioned Indenture.

                                            THE BANK OF NEW YORK
                                            as Trustee


                                            By________________________________
                                                     Authorized Officer



                               REVERSE OF SECURITY


     This  Security  is one of a duly  authorized  issue  of  securities  of the
Company (herein called the "Securities"), issued and to be issued in one or more
series under the Senior Indenture,  dated as of September 1, 1997 (herein called
the  "Indenture"),  between  the  Company  and The Bank of New York,  as Trustee
(herein  called the  "Trustee", which term  includes any  additional  successor
trustee under the Indenture), to which Indenture and all indentures supplemental
thereto  reference  is hereby made for a  statement  of the  respective  rights,
limitation  of rights,  duties and  immunities  thereunder  of the Company,  the
Trustee  and the  Holders  of the  Securities  and of the terms  upon  which the
Securities are, and are to be,  authenticated  and delivered.  Capitalized terms
used but not defined  herein are defined in the  Indenture  and used herein with
the same meanings  ascribed to them therein.  This Security is a Global Security
representing the entire  principal  amount of the series  designated on the face
hereof, limited in aggregate principal amount to $150,000,000.

     The Securities of this series are not redeemable prior to stated maturity.

     The  Securities  of this  series  shall not be  subject  to a sinking  fund
requirement.

     The  Indenture  contains   provisions  for  defeasance  of  (a) the  entire
indebtedness  of  this  Security  and  (b) certain  restrictive  covenants  upon
compliance by the Company with certain conditions set forth therein.

     If an Event of Default with respect to the  Securities of this series shall
occur and be continuing,  the unpaid  principal of the Securities of this series
may be declared  due and  payable in the manner and with the effect  provided in
the Indenture.

     The Indenture  contains  provisions  permitting the Company and the Trustee
with the  consent  of the  Holders  of not less  than a  majority  in  aggregate
principal  amount  of each  series  of  Securities  then  Outstanding  under the
Indenture  and  affected  thereby,  evidenced as provided in the  Indenture,  to
execute  supplemental  indentures  adding any  provisions  to or changing in any
manner  or  eliminating  any  of  the  provisions  of  the  Indenture  or of any
supplemental  indenture  or modifying in any manner the rights of the Holders of
the  Securities of such series;  provided,  however,  that no such  supplemental
indenture shall (i) extend the stated final maturity of any Security,  or reduce
the principal  amount thereof,  or reduce the rate or extend the time of payment
of interest  hereon,  or reduce or alter the method of computation of any amount
payable on redemption,  repayment or purchase by the Company, or change the coin
or currency in which  payments are to be made,  or impair or affect the right of
any  Holder  to  institute  suit  for  enforcement  of  any  payment  hereof  or
(ii) reduce the aforesaid  percentage of any series of such Securities,  without
the consent of the Holders of each  Security  of any series so  affected.  It is
also  provided in the  Indenture  that the  Holders of a majority  in  aggregate
principal  amount of the Securities of any series then Outstanding may on behalf
of the Holders of all of the Securities of such series waive any past default or
Event of Default under the Indenture  and its  consequences  except a default in
the payment of the  principal  of or interest on any of the  Securities  of such

Series.  Any such  consent  or waiver by the  Holder  of this  Security  (unless
revoked as provided in the Indenture)  shall be conclusive and binding upon such
Holder  and  upon  all  future  Holders  and  owners  of this  Security  and any
Securities which may be issued in exchange or substitution herefor, irrespective
of whether or not any notation  thereof is made upon this Security or such other
Securities.

     No reference  herein to the  Indenture and no provision of this Security or
of the Indenture  shall alter or impair the obligation of the Company,  which is
absolute  and  unconditional,  to pay  the  principal  of and  interest  on this
Security at the place, at the respective times, and at the rates and in the coin
or currency herein provided.

     As set forth in, and subject to, the provisions of the Indenture, no Holder
of any Security of this series shall have any right to institute any  proceeding
with respect to the Indenture or for any remedy  thereunder,  unless such Holder
shall have  previously  given to the Trustee  written  notice of default and the
continuance thereof, as provided in the Indenture, and unless the Holders of not
less  than  25% in  principal  amount  of the  Securities  of this  series  then
Outstanding shall have made written request,  and offered reasonable  indemnity,
to the Trustee to institute  such  proceeding as trustee,  and the Trustee shall
have failed to institute such proceeding within 60 days; provided, however, that
such limitations shall not impair the right of a Holder hereof to institute suit
for the  enforcement of payment of the principal of or interest on this Security
on or after the  respective  due dates  expressed  herein without the consent of
such Holder.

     This  Security  shall  be  exchangeable   for  Securities  of  this  series
registered  in the names of Persons  other than the  Depository  with respect to
such series or its nominee  only as provided in this  paragraph.  This  Security
shall be so exchangeable if (i) such  Depository notifies the Company that it is
unwilling,  unable or ineligible to continue as Depository for this Security and
a  successor  Depository  is not  appointed  by the  Company  within  90 days or
(ii) the  Company executes and delivers to the Trustee a written order providing
that this Security  shall be so  exchangeable.  Securities so issued in exchange
for this Security  shall be of the same series and of like tenor,  in authorized
denominations  and in the aggregate  having the same unpaid  principal amount as
this  Security and  registered  in such names as such  Depository  shall direct.
Individual Securities of this series so issued will be issued in registered form
and  denominations,  unless  otherwise  specified by the Company,  of $1,000 and
integral multiples thereof.

     As provided in the Indenture and subject to certain limitations therein set
forth,  the transfer of this Security is  registrable  in the security  register
maintained for that purpose, upon surrender of this Security for registration of
transfer at the office or agency of the Company in any place where the principal
of (and  premium,  if any) and  interest  on this  Security  are  payable,  duly
endorsed  by,  or  accompanied  by a  written  instrument  of  transfer  in form
satisfactory  to the Company and the Trustee duly executed by, the Holder hereof
or its  attorney  duly  authorized  in  writing,  and  thereupon  on or more new
Securities of this series,  and of like tenor, of authorized  denominations  and
for  the  same  aggregate  unpaid  principal  amount,  shall  be  issued  to the
designated  transferee or transferees.  At the date of the original  issuance of
this Security, such 


office or agency of the Company is  maintained  by the Trustee at its  Corporate
Trust Office, 101 Barclay Street, Floor 21 West, New York, New York.

     No service  charge shall be made for any such exchange or  registration  of
transfer,  but the Company may require  payment of a sum sufficient to cover any
tax or other governmental charge payable in connection therewith.

     Prior to due presentment of this Security for registration of transfer, the
Company,  the  Trustee and any agent of the Company or the Trustee may treat the
Person in whose name this  Security is  registered  as the owner  hereof for all
purposes,  whether or not this Security be overdue, and neither the Company, the
Trustee  nor any such agent shall be  affected  by notice to the  contrary.  All
payments  made to or upon the  order of such  registered  Holder  shall,  to the
extent of the sum or sums so paid,  satisfy  and  discharge  the  liability  for
moneys payable on this Security.

     Pursuant  to a  recommendation  promulgated  by the  Committee  on  Uniform
Security Identification  Procedures, the Company has caused a CUSIP number to be
printed  on  this  Security  as  a  convenience   to  the  Holder   hereof.   No
representation  is made as to the  accuracy of such number and  reliance  may be
placed only on the other identifying information printed hereon.

     Interest on this Security  shall be computed on the basis of a 360-day year
comprised of twelve 30-day months.

     All terms used in this Security  which are defined in the  Indenture  shall
have the meanings assigned to them in the Indenture.

     The  Indenture  and this  Security  shall be governed by and  construed  in
accordance with the laws of the State of New York.


                                 ASSIGNMENT FORM


I or we assign and transfer this Security to   




(Print or type name, address and zip code of assignee or transferee)


 
(Insert Social Security or other identifying number of assignee or transferee)

and  irrevocably  appoint  agent to transfer  this  Security on the books of the
Company. The agent may substitute another to act for him.


Dated: ____________                   Signed: ________________________________ 
                                       Sign exactly as name appears above or on
                                       the other side of this Security)



Signature Guarantee:                                                    _______
                           Participant in a recognized Signature Guarantee
                           Medallion Program (or other signature guarantor
                           program reasonably acceptable to the Trustee)