<PAGE>
 
                                                                     EXHIBIT 1.1

                             NUEVO ENERGY COMPANY

                               1,860,000 SHARES

                                 COMMON STOCK


                            UNDERWRITING AGREEMENT


                                                               December 18, 1996


J.P. Morgan Securities Inc.
Donaldson, Lufkin & Jenrette Securities Corporation
Morgan Keegan & Company, Inc.
PaineWebber Incorporated
As Representatives of the several underwriters
 listed in Schedule I hereto
c/o J.P. Morgan Securities Inc.
60 Wall Street
New York, New York  10260

Ladies and Gentlemen:

     The selling stockholders named in Schedule II hereto (the "Selling
Stockholders"), propose to sell to the several Underwriters listed in Schedule I
hereto (the "Underwriters"), for whom you are acting as representatives (the
"Representatives"), an aggregate of 1,860,000 shares of Common Stock, par value
$.01 per share ("Stock"), of Nuevo Energy Company, a Delaware corporation (the
"Company") (the "Underwritten Shares") and, for the sole purpose of covering
over-allotments in connection with the sale of the Underwritten Shares, at the
option of the Underwriters, up to an additional 278,605 shares of Stock (the
"Option Shares").  The Underwritten Shares and the Option Shares are herein
referred to as the "Shares".

     The Company has prepared and filed with the Securities and Exchange
Commission (the "Commission") in accordance with the provisions of the
Securities Act of 1933, as amended, and the rules and regulations of the
Commission thereunder (collectively, the "Securities Act"), a registration
statement, including a base prospectus, relating to the Shares and certain other
securities.  The registration statement as amended at the time when it became
effective on November 25, 1996, including information (if any) deemed to be part
of the registration statement at the time of effectiveness pursuant to Rule 430A
under the Securities Act, is referred to in this Agreement as the "Registration
Statement", and the base prospectus dated November 25, 1996, as supplemented by
the prospectus supplement relating to the Shares, in the 
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form first used to confirm sales of Shares is referred to in this Agreement as
the "Prospectus". If the Company has filed an abbreviated registration statement
pursuant to Rule 462(b) under the Securities Act (the "Rule 462 Registration
Statement"), then any reference herein to the term "Registration Statement"
shall be deemed to include such Rule 462 Registration Statement. Any reference
in this Agreement to the Registration Statement, any preliminary prospectus or
the Prospectus shall be deemed to refer to and include the documents
incorporated by reference therein pursuant to Item 12 of Form S-3 under the
Securities Act, as of the effective date of the Registration Statement or the
date of such preliminary prospectus or the Prospectus, as the case may be, and
any reference to "amend", "amendment" or "supplement" with respect to the
Registration Statement, any preliminary prospectus or the Prospectus shall be
deemed to refer to and include any documents filed after such date under the
Securities Exchange Act of 1934, as amended, and the rules and regulations of
the Commission thereunder (collectively, the "Exchange Act") that are deemed to
be incorporated by reference therein.

     The Selling Stockholders hereby agree with the Underwriters as follows:

     1.   The Selling Stockholders severally agree to sell the Underwritten
Shares to the several Underwriters as hereinafter provided, and each
Underwriter, upon the basis of the representations and warranties herein
contained, but subject to the conditions hereinafter stated, agrees to purchase,
severally and not jointly, from the Selling Stockholders the respective number
of Underwritten Shares set forth opposite such Underwriter's name in Schedule I
hereto at a purchase price per share (the "Purchase Price") of $45.125.

     In addition, the Selling Stockholders severally agree to sell the Option
Shares to the several Underwriters as hereinafter provided, and the Underwriters
on the basis of the representations and warranties herein contained, but subject
to the conditions hereinafter stated, shall have the option to purchase,
severally and not jointly, from United Investors Management Company ("United")
up to 103,605 Option Shares and from The 1818 Fund, L.P. (the "1818 Fund") up to
175,000 Option Shares, in each case at the Purchase Price and for the sole
purpose of covering over-allotments (if any) in the sale of Underwritten Shares
by the several Underwriters; provided, however, that the Underwriters may
exercise such option granted by the 1818 Fund only if the Underwriters have
exercised in full such option granted by United.

     If any Option Shares are to be purchased, the number of Option Shares to be
purchased by each Underwriter shall be the number of Option Shares which bears
the same ratio to the aggre gate number of Option Shares being purchased as the
number of Underwritten Shares set forth opposite the name of such Underwriter in
Schedule I hereto (or such number increased as set forth in Section 9 hereof)
bears to the aggregate number of Underwritten Shares being purchased from the
Selling Stockholders by the several Underwriters, subject, however, to such
adjustments to eliminate any fractional Shares as the Representatives in their
sole discretion shall make.

     The Underwriters may exercise the options to purchase the Option Shares at
any time (but not more than once) on or before the thirtieth day following the
date of this Agreement, by 

                                      -2-
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written notice from the Representatives to the Company and the Selling
Stockholders. Such notice shall identify which option is being exercised and
shall set forth the aggregate number of Option Shares as to which the option is
being exercised and the date and time when the Option Shares are to be delivered
and paid for which may be the same date and time as the Closing Date (as
hereinafter defined) but shall not be earlier than the Closing Date nor later
than the tenth full Business Day (as hereinafter defined) after the date of such
notice (unless such time and date are postponed in accordance with the
provisions of Section 9 hereof). Any such notice shall be given at least two
Business Days (as defined below) prior to the date and time of delivery
specified therein. If both of the options are exercised, they must provide for
the same delivery date.

     2.   The Selling Stockholders and the Company understand that the
Underwriters intend (i) to make a public offering of the Shares as soon after
the parties hereto have executed and delivered this Agreement, as in the
judgment of the Representatives is advisable, and (ii) initially to offer the
Shares upon the terms set forth in the Prospectus.

     3.   Payment for the Shares shall be made by wire transfer in immediately
available funds, in the case of the Underwritten Shares, on December 23, 1996,
or at such other time on the same or such other date, not later than the fifth
Business Day thereafter, as the Representatives and the Selling Stockholders may
agree upon in writing or, in the case of the Option Shares, on the date and time
specified by the Representatives in the written notice of the Underwriters'
election to purchase such Option Shares, such payments to be made to the
accounts specified, no later than noon on the Business Day prior to the Closing
Date or the Additional Closing Date (each as defined below), by the Selling
Stockholders to the Representatives.  The time and date of such payment for the
Underwritten Shares is referred to herein as the "Closing Date" and the time and
date for such payment for the Option Shares, if other than the Closing Date, are
herein referred to as the "Additional Closing Date."  As used herein, the term
"Business Day" means any day other than a day on which banks are permitted or
required to be closed in New York City or Houston, Texas.

     Payment for the Shares to be purchased on the Closing Date or the
Additional Closing Date, as the case may be, shall be made against delivery to
the Representatives for the respective accounts of the several Underwriters of
the Shares to be purchased on such date registered in such names and in such
denominations as the Representatives shall request in writing not later than two
full Business Days prior to the Closing Date or the Additional Closing Date, as
the case may be, with any transfer taxes payable in connection with the transfer
to the Underwriters of the Shares duly paid by the Selling Stockholders.  The
certificates for the Shares will be made available for inspection and packaging
by the Representatives at the office of J.P. Morgan Securities Inc. set forth
above not later than 1:00 P.M., New York City time, on the Business Day prior to
the Closing Date or the Additional Closing Date, as the case may be.

     4.   (a)  The Company represents and warrants to each Underwriter and the
Selling Stockholders that:

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          (i)    no order preventing or suspending the use of any preliminary
     prospectus has been issued by the Commission, and each preliminary
     prospectus filed as part of the Registration Statement as originally filed
     or as part of any amendment thereto, or filed pursuant to Rule 424 under
     the Securities Act, complied when so filed in all material respects with
     the Securities Act, and did not contain an untrue statement of a material
     fact or omit to state a material fact required to be stated therein or
     necessary to make the statements therein, in the light of the circumstances
     under which they were made, not misleading; provided that this
     representation and warranty shall not apply to any statements or omissions
     made in reliance upon and in conformity with information relating to (a)
     any Underwriter furnished to the Company in writing by such Underwriter
     through the Representatives or (b) any Selling Stockholder furnished to the
     Company in writing by such Selling Stockholder, in either case expressly
     for use therein;

          (ii)   no stop order suspending the effectiveness of the Registration
     Statement has been issued and no proceeding for that purpose has been
     instituted or, to the knowledge of the Company, threatened by the
     Commission; and the Registration Statement and Prospectus (as amended or
     supplemented if the Company shall have furnished any amendments or
     supplements thereto) comply, or will comply, as the case may be, in all
     material respects with the Securities Act and do not and will not, as of
     the applicable effective date as to the Registration Statement and any
     amendment thereto, contain any untrue statement of a material fact or omit
     to state any material fact required to be stated therein or necessary to
     make the statements therein not misleading, and the Prospectus, as amended
     or supplemented, if applicable, at the Closing Date or Additional Closing
     Date, as the case may be, will not contain any untrue statement of a
     material fact or omit to state a material fact necessary to make the
     statements therein, in the light of the circumstances under which they were
     made, not misleading; except that the foregoing representations and
     warranties shall not apply to statements or omissions in the Registration
     Statement or the Prospectus made in reliance upon and in conformity with
     information relating to (a) any Underwriter furnished to the Company in
     writing by such Underwriter through the Representatives or (b) any Selling
     Stockholder furnished to the Company in writing by such Selling
     Stockholder, in either case expressly for use therein;

          (iii)  the documents incorporated by reference in the Prospectus, when
     they became effective or were filed with the Commission, as the case may
     be, conformed in all material respects to the requirements of the
     Securities Act or the Exchange Act, as applicable, and as of such time none
     of such documents contained an untrue statement of a material fact or
     omitted to state a material fact necessary to make the statements therein,
     in the light of the circumstances under which they were made, not
     misleading; and any further documents so filed and incorporated by
     reference in the Prospectus, when such documents are filed with the
     Commission, will conform in all material respects to the requirements of
     the Exchange Act, and will not contain an untrue statement of a material
     fact or omit to state a material fact necessary to make the statements
     therein, in the light of the circumstances under which they were made, not
     misleading;

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          (iv)   the financial statements, and the related notes thereto,
     included or incorporated by reference in the Registration Statement and the
     Prospectus present fairly the consolidated financial position of the
     Company and its consolidated subsidiaries as of the dates indicated and the
     results of their operations and changes in their consolidated cash flows
     for the periods specified; said financial statements have been prepared in
     conformity with generally accepted accounting principles applied on a
     consistent basis, and the supporting schedules included or incorporated by
     reference in the Registration Statement present fairly the information
     required to be stated therein; and the pro forma financial information, and
     the related notes thereto, included or incorporated by reference in the
     Registration Statement and the Prospectus has been prepared in accordance
     with the applicable requirements of the Securities Act and the Exchange
     Act, as applicable and is based upon good faith estimates and assumptions
     believed by the Company to be reasonable, and the adjustments used therein
     are appropriate to give pro forma effect to the transactions referenced
     therein; such pro forma information has been prepared on a basis consistent
     with such historical statements, except for the pro forma adjustments
     specified therein, and give effect to assumptions made on a reasonable
     basis and present fairly the historical transactions included or
     incorporated by reference in the Registration Statement and the Prospectus;
     the other financial and statistical information and data included or
     incorporated by reference in the Registration Statement and the Prospectus,
     historical and pro forma, are, in all material respects, accurately
     presented and prepared on a basis consistent with such financial statements
     and the books and records of the Company;

          (v)    since the respective dates as of which information is given in
     the Registration Statement and the Prospectus, there has not been any
     change in the capital stock or long-term debt of the Company or any of its
     subsidiaries, or any material adverse change, or any development involving
     a prospective material adverse change, in or affecting the general affairs,
     business, prospects, management, financial position, stockholders' equity
     or results of operations of the Company and its subsidiaries, taken as a
     whole, otherwise than as set forth, incorporated by reference or
     contemplated in the Prospectus; and except as set forth, incorporated by
     reference or contemplated in the Prospectus, neither the Company nor any of
     its subsidiaries has entered into any transaction or agreement (whether or
     not in the ordinary course of business) material to the Company and its
     subsidiaries taken as a whole;

          (vi)   the Company has been duly incorporated and is validly existing
     as a corporation in good standing under the laws of its jurisdiction of
     incorporation, with power and authority (corporate and other) to own its
     properties and conduct its business as described in the Prospectus, and has
     been duly qualified as a foreign corporation for the transaction of
     business and is in good standing under the laws of each other jurisdiction
     in which it owns or leases properties, or conducts any business, so as to
     require such qualification, other than where the failure to be so qualified
     or in good standing would not have a material adverse effect on the Company
     and its subsidiaries, taken as a whole;

                                      -5-
<PAGE>

          (vii)  each of the Company's subsidiaries has been duly incorporated
     and is validly existing as a corporation under the laws of its jurisdiction
     of incorporation, with power and authority (corporate and other) to own its
     properties and conduct its business as described in the Prospectus, and has
     been duly qualified as a foreign corporation for the transaction of
     business and is in good standing under the laws of each jurisdiction in
     which it owns or leases properties, or conducts any business, so as to
     require such qualification, other than where the failure to be so qualified
     or in good standing would not have a material adverse effect on the Company
     and its subsidiaries taken as a whole; and all the outstanding shares of
     capital stock of each corporate subsidiary of the Company have been duly
     authorized and validly issued, are fully-paid and non-assessable, and,
     except for 20%, 50% and 27.88% of the outstanding shares of common stock of
     Bright Star Gathering, Inc., Sepulveda Oil & Gas Company and The Los
     Angeles Oil Company, respectively, and as otherwise set forth or
     incorporated by reference in the Prospectus, are owned by the Company,
     directly or indirectly, free and clear of all liens, encumbrances, security
     interests and claims;
 
          (viii) this Agreement has been duly authorized, executed and
     delivered by the Company;

          (ix)   the Company has an authorized capitalization as set forth in
     the Prospectus and such authorized capital stock conforms as to legal
     matters to the description thereof set forth in the Prospectus, and all of
     the outstanding shares of capital stock of the Company have been duly
     authorized and validly issued, are fully-paid and non-assessable and are
     not subject to any preemptive or similar rights; and, except as described
     or incorporated by reference in or contemplated by the Prospectus, there
     are no outstanding rights (including, without limitation, pre-emptive
     rights), warrants or options to acquire, or instruments convertible into or
     exchangeable for, any shares of capital stock or other equity interest in
     the Company or any of its subsidiaries, or any contract, commitment,
     agreement, understanding or arrangement of any kind relating to the
     issuance of any capital stock of the Company or any such subsidiary, any
     such convertible or exchangeable securities or any such rights, warrants or
     options;

          (x)    at the Closing Date, the Shares to be sold to the Underwriters
     hereunder will have been duly authorized, issued and are fully paid and
     non-assessable and conform to the descriptions thereof in the Prospectus;
     and the Shares are not subject to any preemptive or similar rights;

          (xi)   neither the Company nor any of its subsidiaries is, or with the
     giving of notice or lapse of time or both would be, in violation of or in
     default under, its respective certificate of incorporation or by-laws or
     any indenture, mortgage, deed of trust, loan agreement or other agreement
     or instrument to which the Company or any of its subsidiaries is a party or
     by which it or any of them or any of their respective properties is bound,
     except for violations and defaults which individually and in the aggregate
     are not 

                                      -6-
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     material to the Company and its subsidiaries taken as a whole; the
     performance by the Company of its obligations under this Agreement and the
     consummation of the transactions contemplated herein will not conflict with
     or result in a breach of any of the terms or provisions of, or constitute a
     default under, any indenture, mortgage, deed of trust, loan agreement or
     other agreement or instrument to which the Company or any of its
     subsidiaries is a party or by which the Company or any of its subsidiaries
     is bound or to which any of the property or assets of the Company or any of
     its subsidiaries is subject, nor will any such action result in any
     violation of the provisions of the Certificate of Incorporation or the By-
     laws of the Company or any applicable law or statute or any order, rule or
     regulation of any court or governmental agency or body having jurisdiction
     over the Company, its subsidiaries or any of their respective properties;
     and no consent, approval, authorization, order, license, registration or
     qualification of or with any such court or governmental agency or body is
     required for the sale of the Shares or the consummation by the Company of
     the transactions contemplated by this Agreement, except such consents,
     approvals, authorizations, orders, licenses, registrations or
     qualifications as have been obtained under the Securities Act and as may be
     required under state securities or blue sky laws in connection with the
     purchase and distribution of the Shares by the Underwriters;

          (xii)  other than as set forth, incorporated by reference or
     contemplated in the Prospectus, there are no legal or governmental
     investigations, actions, suits or proceedings pending or, to the knowledge
     of the Company, threatened against or affecting the Company or any of its
     subsidiaries or any of their respective properties or to which the Company
     or any of its subsidiaries is or may be a party or to which any property of
     the Company or any of its subsidiaries is or may be the subject which, if
     determined adversely to the Company or any of its subsidiaries could,
     individually or in the aggregate, reasonably be expected to have a material
     adverse effect on the general affairs, business, prospects, management,
     financial position, stockholders' equity or results of operations of the
     Company and its subsidiaries, taken as a whole, and, to the best of the
     Company's knowledge, no such proceedings are threatened or contemplated by
     governmental authorities or threatened by others;

          (xiii) the Company and its subsidiaries have good and indefeasible
     title in fee simple to all items of real property and good and marketable
     title to all personal property owned by them, in each case free and clear
     of all liens, encumbrances and defects except such as are described or
     referred to in the Prospectus or such as do not materially affect the value
     of such property and do not interfere with the use made or proposed to be
     made of such property by the Company and its subsidiaries; and any property
     held under lease by the Company and its subsidiaries are held by them under
     valid, existing and enforceable leases with such exceptions as are not
     material and do not interfere with the use made or proposed to be made of
     such property by the Company or its subsidiaries;

          (xiv)  no relationship, direct or indirect, exists between or among
     the Company or any or its subsidiaries on the one hand, and the directors,
     officers, stockholders, 

                                      -7-
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     customers or suppliers of the Company or any of its subsidiaries on the
     other hand, which is required by the Securities Act to be described in the
     Registration Statement and the Prospectus which is not so described or
     incorporated by reference therein;

          (xv)   no person (other than the Selling Stockholders) has the right
     to require the Company to register any securities for offering and sale
     under the Securities Act by reason of the filing of the Registration
     Statement with the Commission or the issue and sale of the Shares;

          (xvi)  the Company is not an "investment company" or entity
     "controlled" by an "investment company", as such terms are defined in the
     Investment Company Act of 1940, as amended (the "Investment Company Act");

          (xvii) the Company has complied with all provisions of Section
     517.075, Florida Statutes (Chapter 92-198, Laws of Florida) relating to
     doing business with the Government of Cuba or with any person or affiliate
     located in Cuba;

          (xviii) KPMG Peat Marwick LLP, who have certified certain financial
     statements of the Company and its subsidiaries, are independent public
     accountants as required by the Securities Act;

          (xix)  the Company and its subsidiaries have filed all federal, state,
     local and foreign tax returns which have been required to be filed and have
     paid all taxes shown thereon and all assessments received by them or any of
     them to the extent that such taxes have become due and are not being
     contested in good faith; and, except as disclosed in the Registration
     Statement and the Prospectus, there is no tax deficiency which has been or
     might reasonably be expected to be asserted or threatened against the
     Company or any subsidiary;

          (xx)   the Company has not taken nor will it take, directly or
     indirectly, any action designed to, or that might be reasonably expected
     to, cause or result in stabilization or manipulation of the price of the
     Common Stock;

          (xxi)  each of the Company and its subsidiaries owns, possesses or has
     obtained all material licenses, permits, certificates, consents, orders,
     approvals and other authorizations from, and has made all declarations and
     filings with, all federal, state, local and other governmental authorities
     (including foreign regulatory agencies), all self-regulatory organizations
     and all courts and other tribunals, domestic or foreign, necessary to own
     or lease, as the case may be, and to operate its properties and to carry on
     its business as conducted as of the date hereof, and neither the Company
     nor any such subsidiary has received any actual notice of any proceeding
     relating to revocation or modification of any such license, permit,
     certificate, consent, order, approval or other authorization, except as
     described in the Registration Statement and the Prospectus; and each of the
     Company and its subsidiaries is in compliance with all laws and regulations

                                      -8-
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     relating to the conduct of its business as conducted as of the date hereof,
     except where noncompliance with such laws and regulations would not have a
     material adverse effect on the Company and its subsidiaries, taken as a
     whole;
 
          (xxii) there are no existing or, to the best knowledge of the
     Company, threatened labor disputes with the employees of the Company or any
     of its subsidiaries which are likely to have a material adverse effect on
     the Company and its subsidiaries, taken as a whole;

          (xxiii) the Company and its subsidiaries (i) are in compliance with
     any and all applicable foreign, federal, state and local laws and
     regulations relating to the protection of human health and safety, the
     environment or hazardous or toxic substances or wastes, pollutants or
     contaminants ("Environmental Laws"), (ii) have received all permits,
     licenses or other approvals required of them under applicable Environmental
     Laws to conduct their respective businesses and (iii) are in compliance
     with all terms and conditions of any such permit, license or approval,
     except where such noncompliance with Environmental Laws, failure to receive
     required permits, licenses or other approvals or failure to comply with the
     terms and conditions of such permits, licenses or approvals would not,
     singly or in the aggregate, have a material adverse effect on the Company
     and its subsidiaries, taken as a whole;

          (xxiv) in the ordinary course of its business, the Company conducts a
     periodic review of the effect of Environmental Laws on the business,
     operations and properties of the Company and its subsidiaries, in the
     course of which it identifies and evaluates associated costs and
     liabilities (including, without limitation, any capital or operating
     expenditures required for clean-up, closure of properties or compliance
     with Environmental Laws or any permit, license or approval, any related
     constraints on operating activities and any potential liabilities to third
     parties).  On the basis of such review, the Company has reasonably
     concluded that such associated costs and liabilities would not, singly or
     in the aggregate, have a material adverse effect on the Company and its
     subsidiaries, taken as a whole;
 
          (xxv)  each employee benefit plan, within the meaning of Section 3(3)
     of the Employee Retirement Income Security Act of 1974, as amended,
     ("ERISA") that is maintained, administered or contributed to by the Company
     or any of its affiliates for employees or former employees of the Company
     and its affiliates has been maintained in compliance with its terms and the
     requirements of any applicable statutes, orders, rules and regulations,
     including but not limited to ERISA and the Internal Revenue Code of 1986,
     as amended, ("Code").  No prohibited transaction, within the meaning of
     Section 406 of ERISA or Section 4975 of the Code has occurred with respect
     to any such plan excluding transactions effected pursuant to a statutory or
     administrative exemption.  For each such plan which is subject to the
     funding rules of Section 412 of the Code or Section 302 of ERISA no
     "accumulated funding deficiency" as defined in Section 412 of the Code has
     been incurred, whether or not waived, and the fair market value of the
     assets of 

                                      -9-
<PAGE>
 
     each such plan (excluding for these purposes accrued but unpaid
     contributions) exceeded the present value of all benefits accrued under
     such plan determined using reasonable actuarial assumptions;

          (xxvi) the Company maintains a system of internal accounting control
     sufficient to provide reasonable assurance that (i) transactions are
     executed in accordance with management's general or specific authorization;
     (ii) transactions are recorded as necessary to permit preparation of
     financial statements in conformity with generally accepted accounting
     principles and to maintain accountability for assets; (iii) access to
     assets is permitted only in accordance with management's general or
     specific authorization; and (iv) the recorded accountability for assets is
     compared with existing assets at reasonable intervals and appropriate
     action is taken with respect to any differences;

          (xxvii) there is no document or contract of a character required to
     be described in the Registration Statement or the Prospectus or to be filed
     as an exhibit to the Registration Statement which is not described or filed
     as required.  All such contracts to which the Company or any subsidiary is
     a party have been duly authorized, executed and delivered by the Company or
     such subsidiary, constitute valid and binding agreements of the Company or
     such subsidiary and are enforceable against the Company or such subsidiary
     in accordance with the terms thereof, except as may be limited by
     bankruptcy, insolvency, reorganization or other laws of general application
     relating to or affecting creditors' rights generally or the availability of
     equitable remedies, regardless of whether such enforcement is considered in
     a proceeding in equity or at law;

          (xxviii) the Company maintains insurance policies currently in effect,
     including levels of deductibles, that are customary in the oil and gas
     industry.  Such policies provide coverage for operations of the Company and
     its subsidiaries in amounts and covering such risks as the Company believes
     is necessary to conduct its business;

          (xxix) neither the Company nor any of its subsidiaries nor, to the
     Company's knowledge, any employee or agent of the Company or any subsidiary
     has made any payment of funds of the Company or any subsidiary or received
     or retained any funds in violation of any law, rule or regulation;

          (xxx)  except as described or incorporated by reference in the
     Prospectus, as of the date hereof, (i) all royalties, rentals, deposits and
     other amounts due on the oil and gas properties of the Company have been
     properly and timely paid, and no proceeds from the sale or production
     attributable to the oil and gas properties of the Company are currently
     being held in suspense by any purchaser thereof, except where such amounts
     due could not, singly or in the aggregate, have a material adverse effect
     on the Company and its subsidiaries, taken as a whole, and (ii) there are
     no claims under take-or-pay contracts pursuant to which natural gas
     purchasers have any make-up rights affecting the interests of the Company
     in its oil and gas properties, except where such claims could not, singly

                                      -10-
<PAGE>
 
     or in the aggregate, have a material adverse effect on the Company and its
     subsidiaries, taken as a whole;

          (xxxi) except as described or incorporated by reference in the
     Prospectus, as of the date hereof, the aggregate undiscounted monetary
     liability of the Company for petroleum taken or received under any
     operating or gas balancing and storage agreement relating to its oil and
     gas properties that permits any person to receive any portion of the
     interest of the Company in any petroleum or to receive cash or other
     payments to balance any disproportionate allocation of petroleum could not,
     singly or in the aggregate, have a material adverse effect on the Company
     and its subsidiaries, taken as a whole; and

          (xxxii) neither the Company nor any subsidiary of the Company is a
     "holding company" or a "subsidiary company" of a "holding company," or an
     "affiliate" of a "holding company" or of a "subsidiary company" of a
     "holding company," or a "public utility" within the meaning of the Public
     Utility Holding Company Act of 1935, as amended.

          (b)  Each Selling Stockholder represents and warrants to, and agrees
with, the Underwriters and the Company that:

          (i)    except as required by the Act or state securities or Blue sky
     laws, all consents, approvals, authorizations and orders necessary for the
     execution and delivery by such Selling Stockholder of this Agreement and
     for the sale and delivery of the Shares to be sold by such Selling
     Stockholder have been obtained; such Selling Stockholder has full power and
     authority to enter into this Agreement and to sell, assign, transfer and
     deliver the Shares to be sold by such Selling Stockholders hereunder; and
     this Agreement has been duly authorized, executed and delivered by such
     Selling Stockholder;

          (ii)   the execution, delivery and performance of this Agreement by
     such Selling Stockholder, the sale of the Shares and the consummation by
     such Selling Stockholder of the transactions contemplated hereby will not
     conflict with or result in a breach or violation of any of the terms or
     provisions of, or constitute a default under, any indenture, mortgage, deed
     of trust, loan agreement or other agreement or instrument to which such
     Selling Stockholder is a party or by which such Selling Stockholder is
     bound, or to which any of the property or assets of such Selling
     Stockholder is subject, or any statute or any order, rule or regulation of
     any court or governmental agency having jurisdiction over such Selling
     Stockholder or its property;

          (iii)  at the time of delivery of the Shares, such Selling Stockholder
     will have good and valid title to the Shares to be sold by such Selling
     Stockholder on the Closing Date or the Additional Closing Date, as the case
     may be, free and clear of all liens, encumbrances, equities or claims
     (other than the interests of the Underwriters under this Agreement); and,
     upon delivery of such Shares and payment therefor pursuant hereto, good and
     valid title to such Shares, free and clear of all liens, encumbrances,
     equities or 

                                      -11-
<PAGE>
 
     claims, will pass to the Underwriters;

          (iv)   for a period of 90 days after the date hereof, such Selling
     Stockholder shall not offer, pledge, sell, contract to sell, sell any
     option or contract to purchase, purchase any option or contract to sell,
     grant any option, right or warrant to purchase or otherwise transfer,
     dispose of, directly or indirectly, any shares of Stock or any securities
     convertible into or exercisable or exchangeable for stock, without the
     prior written consent of J.P. Morgan Securities Inc.;

          (v)    such Selling Stockholder does not have any knowledge without
     independent investigation that the Registration Statement or the Prospectus
     (or any amendment or supplement thereto) contains any untrue statement of a
     material fact or omits to state a material fact required to be stated
     therein or necessary to make the statements therein not misleading; and

          (vi)   such Selling Stockholder has not taken and will not take,
     directly or indirectly, any action which is designed to or which has
     constituted or which might reasonably be expected to cause or result in
     stabilization or manipulation of the price or any security of the Company
     to facilitate the sale or resale of the Shares.

     5.   The Company covenants and agrees with each of the several Underwriters
as follows:

          (a)  to use its best efforts, if required, to file the final
     Prospectus with the Commission within the time periods specified by Rule
     424(b) and Rule 430A under the Securities Act and to file promptly all
     reports and any definitive proxy or information statements required to be
     filed by the Company with the Commission pursuant to Section 13(a), 13(c),
     14 or 15(d) of the Exchange Act subsequent to the date of the Prospectus
     and for so long as the delivery of a prospectus is required in connection
     with the offering or sale of the Shares; and to furnish copies of the
     Prospectus to the Underwriters in New York City prior to 10:00 a.m., New
     York City time, on the Business Day next succeeding the date of this
     Agreement in such quantities as the Representatives may reasonably request;

          (b)  to deliver, at the expense of the Company, to the Representatives
     five signed copies of the Registration Statement (as originally filed) and
     each amendment thereto, in each case including exhibits and documents
     incorporated by reference therein, and to each other Underwriter a
     conformed copy of the Registration Statement (as originally filed) and each
     amendment thereto, in each case without exhibits but including the
     documents incorporated by reference therein and, during the period
     mentioned in paragraph 5(e) below, to each of the Underwriters as many
     copies of the Prospectus (including all amendments and supplements thereto)
     and documents incorporated by refer ence therein as the Representatives may
     reasonably request;

                                      -12-
<PAGE>
 
          (c)  before filing any amendment or supplement to the Registration
     Statement or the Prospectus, whether before or after the time the
     Registration Statement becomes effective, to furnish to the Representatives
     a copy of the proposed amendment or supplement for review and not to file
     any such proposed amendment or supplement to which the Representatives
     reasonably object;

          (d)  to advise the Representatives promptly, and to confirm such
     advice in writing (i) when any amendment to the Registration Statement has
     been filed or becomes effective, (ii) when any supplement to the Prospectus
     or any amended Prospectus has been filed and to furnish the Representatives
     with copies thereof, (iii) of any request by the Commission for any
     amendment to the Registration Statement or any amendment or supplement to
     the Prospectus or for any additional information, (iv) of the issuance by
     the Commission of any stop order suspending the effectiveness of the
     Registration Statement or of any order preventing or suspending the use of
     any preliminary prospectus or the Prospectus or the initiation or
     threatening of any proceeding for that purpose, (v) of the occurrence of
     any event, within the period referenced in paragraph 5(e) below, as a
     result of which the Prospectus as then amended or supplemented would
     include an untrue statement of a material fact or omit to state any
     material fact necessary in order to make the statements therein, in the
     light of the circumstances when the Prospectus is delivered to a purchaser,
     not misleading, and (vi) of the receipt by the Company of any notification
     with respect to any suspension of the qualification of the Shares for offer
     and sale in any jurisdiction or the initiation or threatening of any
     proceeding for such purpose; and to use its best efforts to prevent the
     issuance of any such stop order, or of any order preventing or suspending
     the use of any preliminary prospectus or the Prospectus, or of any order
     suspending any such qualification of the Shares, or notification of any
     such order thereof and, if issued, to obtain as soon as possible the
     withdrawal thereof;

          (e)  if, during such period of time after the first date of the public
     offering of the Shares as in the opinion of counsel for the Underwriters a
     prospectus relating to the Shares is required by law to be delivered in
     connection with sales by the Underwriters or any dealer, any event shall
     occur as a result of which it is necessary to amend or supplement the
     Prospectus in order to make the statements therein, in the light of the
     circumstances when the Prospectus is delivered to a purchaser, not
     misleading, or if it is necessary to amend or supplement the Prospectus to
     comply with law, forthwith to prepare and furnish, at the expense of the
     Company, to the Underwriters and to the dealers (whose names and addresses
     the Representatives will furnish to the Company) to which Shares may have
     been sold by the Representatives on behalf of the Underwriters and to any
     other dealers upon request, such amendments or supplements to the
     Prospectus as may be necessary so that the statements in the Prospectus as
     so amended or supplemented will not, in the light of the circumstances when
     the Prospectus is delivered to a purchaser, be misleading or so that the
     Prospectus will comply with law;

          (f)  to endeavor to qualify the Shares for offer and sale under the
     securities or blue sky laws of such jurisdictions as the Representatives
     shall reasonably request and to 

                                      -13-
<PAGE>
 
     continue such qualification in effect so long as reasonably required for
     distribution of the Shares; provided that the Company shall not be required
     to file a general consent to service of process in any jurisdiction;

          (g)  to make generally available to its security holders and to the
     Representatives as soon as practicable an earnings statement covering a
     period of at least twelve months beginning with the first fiscal quarter of
     the Company occurring after the effective date of the Registration
     Statement, which shall satisfy the provisions of Section 11(a) of the
     Securities Act and Rule 158 of the Commission promulgated thereunder;

          (h)  for five years following the Closing Date, to furnish to the
     Representatives copies of all reports or other communications (financial or
     other) furnished to holders of the Shares, and copies of any reports and
     financial statements furnished to or filed with the Commission or any
     national securities exchange;

          (i)  for a period of 90 days after the date hereof, not to (i) offer,
     pledge, sell, contract to sell, sell any option or contract to purchase,
     purchase any option or contract to sell, grant any option, right or warrant
     to purchase or otherwise transfer or dispose of, directly or indirectly,
     any shares of Stock or any securities convertible into or exercisable or
     exchangeable for Stock or (ii) enter into any swap or other agreement that
     transfers, in whole or in part, any of the economic consequences of
     ownership of the Stock, whether any such transaction described in clause
     (i) or (ii) above is to be settled by delivery of Stock or such other
     securities, in cash or otherwise, without the prior written consent of J.P.
     Morgan Securities Inc.; provided that, notwithstanding the foregoing,
     during such period (A) the Company may issue the $2.875 Term Convertible
     Securities, Series A ("TECONS"), the 5.75% Convertible Subordinated
     Debentures due December 15, 2026 (the "Convertible Debentures") and the
     Guarantee of the TECONS, (B) the Company may issue Stock upon conversion of
     any TECONS or Convertible Debentures, (C) the Company may issue Stock
     pursuant to existing stock incentive plans, (D) the Company may issue Stock
     upon conversion of the 7% Cumulative Convertible Preferred Stock and (E)
     the Company may issue Stock or other rights to acquire Stock as
     consideration for acquired businesses, provided any such shares or rights
     are subject to resale restrictions equivalent to those held by directors of
     the Company;

          (j)  to use its best efforts to maintain the listing of the Shares on
     the New York Stock Exchange (the "Exchange");

          (k)  whether or not the transactions contemplated in this Agreement
     are consummated or this Agreement is terminated, to pay or cause to be paid
     all costs and expenses incident to the performance of its obligations
     hereunder, including without limiting the generality of the foregoing, all
     costs and expenses (i) incident to the preparation, issuance, execution and
     delivery of the Shares, (ii) incident to the preparation, printing and
     filing under the Securities Act of the Registration Statement, the
     Prospectus and any preliminary prospectus (including in each case all
     exhibits, 

                                      -14-
<PAGE>
 
     amendments and supplements thereto), (iii) incurred in connection with the
     registration or qualification of the Shares under the laws of such
     jurisdictions as the Representatives may designate (including fees of
     counsel for the Underwriters and its disbursements), (iv) in connection
     with the listing of the Shares on the Exchange, (v) related to the filing
     with, and clearance of the offering by, the National Association of
     Securities Dealers, Inc., (vi) in connection with the printing (including
     word processing and duplication costs) and delivery of this Agreement, the
     preliminary and supplemental blue sky memoranda and the furnishing to the
     Underwriters and dealers of copies of the Registration Statement and the
     Prospectus, including mailing and shipping, as herein provided, (vii) the
     cost of preparing stock certificates, (ix) the cost and charges of any
     transfer agent and any registrar and (x) the fees and expenses of the
     Company's accountants, engineers and counsel to the Company and the Selling
     Stockholders.

     6.   The several obligations of the Underwriters hereunder to purchase the
Shares on the Closing Date or the Additional Closing Date, as the case may be,
are subject to the performance by the Company and the Selling Stockholders of
their respective obligations hereunder and to the following additional
conditions:

          (a)  the Registration Statement shall be effective on the date hereof
     (or if a post-effective amendment is required to be filed under the
     Securities Act, such post-effective amendment shall have become effective
     not later than 5:00 p.m., New York City time, on the date hereof); and no
     stop order suspending the effectiveness of the Registration Statement or
     any post-effective amendment shall be in effect, and no proceedings for
     such purpose shall be pending before or threatened by the Commission; the
     Prospectus shall have been filed with the Commission pursuant to Rule
     424(b) within the applicable time period prescribed for such filing by the
     rules and regulations under the Securities Act and in accordance with
     Section 5(a) hereof; and all requests for additional information shall have
     been complied with to the satisfaction of the Representatives;

          (b)  the representations and warranties of the Company and the Selling
     Stockholders contained herein are true and correct on and as of the Closing
     Date or the Additional Closing Date, as the case may be, as if made on and
     as of the Closing Date or the Additional Closing Date, as the case may be,
     and the Company shall have complied with all agreements and all conditions
     on its part to be performed or satisfied hereunder at or prior to the
     Closing Date or the Additional Closing Date, as the case may be;

          (c)  subsequent to the execution and delivery of this Agreement and
     prior to the Closing Date or the Additional Closing Date, as the case may
     be, there shall not have occurred any downgrading, nor shall any notice
     have been given of (i) any downgrading, (ii) any intended or potential
     downgrading or (iii) any review or possible change that does not indicate
     an improvement, in the rating accorded any securities of or guaranteed by
     the Company by any "nationally recognized statistical rating organization,"
     as such term is defined for purposes of Rule 436(g)(2) under the Securities
     Act;

                                      -15-
<PAGE>
 
          (d)  since the respective dates as of which information is given in
     the Prospectus there shall not have been any change in the capital stock or
     long-term debt of the Company or any of its subsidiaries or any material
     adverse change, or any development involving a prospective material adverse
     change, in or affecting the general affairs, business, prospects,
     management, financial position, stockholders' equity or results of
     operations of the Company and its subsidiaries, taken as a whole, otherwise
     than as set forth or contemplated in the Prospectus, the effect of which in
     the judgment of the Representatives makes it impracticable or inadvisable
     to proceed with the public offering or the delivery of the Shares on the
     Closing Date or the Additional Closing Date, as the case may be, on the
     terms and in the manner contemplated in the Prospectus; and neither the
     Company nor any of its subsidiaries has sustained since the date of the
     latest audited financial statements included or incorporated by reference
     in the Prospectus any material loss or interference with its business from
     fire, explosion, flood or other calamity, whether or not covered by
     insurance, or from any labor dispute or court or governmental action, order
     or decree, otherwise than as set forth or contemplated in the Prospectus;

          (e)  the Representatives shall have received on and as of the Closing
     Date or the Additional Closing Date, as the case may be, a certificate of
     an executive officer of the Company, with specific knowledge about the
     Company's financial matters, satisfactory to the Representatives to the
     effect set forth in subsections (a) through (d) (with respect to the
     respective representations, warranties, agreements and conditions of the
     Company) of this Section and to the further effect that there has not
     occurred any material adverse change, or any development involving a
     prospective material adverse change, in or affecting the general affairs,
     business, prospects, management, financial position, stockholders' equity
     or results of operations of the Company and its subsidiaries, taken as a
     whole, from that set forth or contemplated in the Registration Statement;

          (f)  Butler & Binion, L.L.P., counsel for the Company, shall have
     furnished to the Representatives their written opinion, dated the Closing
     Date or the Additional Closing Date, as the case may be, in form and
     substance reasonably satisfactory to the Representatives, to the effect
     that:

               (i)    the Company has been duly incorporated and is validly
          existing as a corporation in good standing under the laws of its
          jurisdiction of incorporation, with corporate power and authority to
          own its properties and conduct its business as described in the
          Prospectus;

               (ii)   the Company has been duly qualified as a foreign
          corporation for the transaction of business and is in good standing
          under the laws of each other jurisdiction in which it owns or leases
          properties, or conducts any business, so as to require such
          qualification, other than where the failure to be so qualified or in
          good standing would not have a material adverse effect on the Company
          and its 

                                      -16-
<PAGE>
 
          subsidiaries, taken as a whole;

               (iii)  each of the Company's subsidiaries has been duly
          incorporated and is validly existing as a corporation under the laws
          of its jurisdiction of incorpora tion with power and authority
          (corporate and other) to own its properties and conduct its business
          as described in the Prospectus and has been duly qualified as a
          foreign corporation for the transaction of business and is in good
          standing under the laws of each other jurisdiction in which it owns or
          leases properties, or conducts any business, so as to require such
          qualification, other than where the failure to be so qualified and in
          good standing would not have a material adverse effect on the Company
          and its subsidiaries, taken as a whole; and the Company is the sole
          record owner, directly or indirectly, of all of the capital stock or
          equity interest, as the case may be, of each of its subsidiaries,
          other than Bright Star Gathering, Inc., of which the Company owns 80%
          of the outstanding shares of common stock;

               (iv)   other than as set forth or contemplated in the Prospectus,
          to the best of such counsel's knowledge, there are no legal or
          governmental investigations, actions, suits or proceedings pending or
          threatened against or affecting the Company or any of its subsidiaries
          or any of their respective properties or to which the Company or any
          of its subsidiaries is or may be a party or to which any property of
          the Company or its subsidiaries is or may be the subject which, if
          determined adversely to the Company or any of its subsidiaries, could
          individually or in the aggregate reasonably be expected to have a
          material adverse effect on the general affairs, business, prospects,
          management, financial position, stockholders' equity or results of
          operations of the Company and its subsidiaries, taken as a whole; to
          the best of such counsel's knowledge, no such proceedings are
          threatened or contemplated by governmental authorities or threat ened
          by others; and such counsel does not know of any statutes,
          regulations, contracts or other documents that are required to be
          described in the Registration Statement or Prospectus or to be filed
          as exhibits to the Registration Statement that are not described or
          filed as required;

               (v)    this Agreement has been duly authorized, executed and
          delivered by the Company;

               (vi)   the authorized capital stock of the Company conforms as to
          legal matters in all material respects to the description thereof
          contained in the Prospectus;

               (vii)  all of the issued shares of capital stock of the Company
          (including the Shares being delivered to the Underwriters on the
          Closing Date or the Additional Closing Date, as the case may be,
          against payment therefor in accordance with the Agreement) have been
          duly authorized and are validly issued, 

                                      -17-
<PAGE>
 
          fully paid and non-assessable;

               (viii) the statements in the Prospectus under "Description of
          Capital Stock," "Certain Anti-Takeover Provisions" and "Underwriting,"
          and in the Registration Statement in Item 15, insofar as such
          statements constitute a summary of the terms of the Stock, legal
          matters or documents or proceedings referred to therein, when taken
          together with information incorporated by reference therein, fairly
          present the information called for with respect to such terms, legal
          matters, documents or proceedings in all material respects;
 
               (ix)   the Registration Statement and the Prospectus and any
          amendments and supplements thereto (other than the financial
          statements and related schedules therein and other financial and
          statistical data, as to which such counsel need express no opinion)
          comply as to form in all material respects with the requirements of
          the Securities Act and nothing has come to such counsel's attention
          that would cause them to believe that (other than the financial
          statements and related schedules therein and other financial and
          statistical data, as to which such counsel need express no belief) the
          Registration Statement did not contain any untrue statement of a
          material fact or omitted to state a material fact required to be
          stated therein or necessary to make the statements therein not
          misleading, or that the Prospectus, as amended or supplemented, if
          applicable, does not contain any untrue statement of a material fact
          or omit to state a material fact necessary in order to make the
          statements therein, in the light of the circumstances under which they
          were made, not misleading;

               (x)    the performance by the Company of its obligations under
          this Agreement and the consummation of the transactions contemplated
          herein will not result in a breach of or a default under, any material
          indenture, mortgage, deed of trust, loan agreement or other agreement
          or instrument known to such counsel to which the Company or any of its
          subsidiaries is a party or by which the Company or any of its
          subsidiaries is bound or to which any of the property or assets of the
          Company or any of its subsidiaries is subject, nor will any such
          action result in any violation of the provisions of the Certificate of
          Incorporation or the By-Laws of the Company or any applicable law or
          statute or, to the best of such counsel's knowledge, any order, rule
          or regulation of any court or governmental agency or body having
          jurisdiction over the Company, its subsidiaries or any of their respec
          tive properties (except that such counsel need express no opinion as
          to securities or anti-fraud laws);

               (xi)   no consent, approval, authorization, order, license,
          registration or qualification of or with any court or governmental
          agency or body is required for the sale of the Shares or the
          consummation of the other transactions contemplated by this Agreement,
          except such consents, approvals, authorizations, orders, licenses,
          registrations or qualifications as have been obtained under the
          Securities 

                                      -18-
<PAGE>
 
          Act and as may be required under state securities or blue sky laws in
          connection with the purchase and distribution of the Shares by the
          Underwriters;
 
               (xii)  the Company is not an "investment company" or entity
          "controlled" by an "investment company", as such terms are defined in
          the Investment Company Act;

               (xiii) the documents incorporated by reference in the Prospectus
          or any further amendment or supplement thereto made by the Company
          prior to the Closing Date or the Additional Closing Date, as the case
          may be, (other than the financial statements and related schedules
          therein and other financial and statistical data, as to which such
          counsel need express no opinion), when they became effective or were
          filed with the Commission, as the case may be, complied as to form in
          all material respects with the requirements of the Securities Act or
          the Exchange Act, as applicable, and the rules and regulations of the
          Commission thereunder; and they have no reason to believe that any of
          such documents, when such documents became effective or were so filed,
          as the case may be contained, in the case of a registration statement
          which became effective under the Securities Act, an untrue statement
          of a material fact or omitted to state a material fact required to be
          stated therein or necessary to make the statements therein not
          misleading, or, in the case of other documents which were filed under
          the Exchange Act with the Commission, an untrue statement of a
          material fact or omitted to state a material fact necessary in order
          to make the statements therein, in the light of the circumstances
          under which they were made when such documents were so filed, not
          misleading; and

               (xiv)  the Registration Statement has become effective under the
          Securities Act, and, to such counsel's knowledge, no stop order
          suspending the effectiveness of the Registration Statement or any part
          thereof has been issued and no proceedings for that purpose have been
          instituted or are pending under the Securities Act.

          In rendering such opinions, such counsel may rely (A) as to matters
     involving the application of laws other than the laws of the United States
     and the States of Texas, Delaware and New York, to the extent such counsel
     deems proper and to the extent speci fied in such opinion, if at all, upon
     an opinion or opinions (in form and substance reasonably satisfactory to
     Underwriters' counsel) of other counsel reasonably acceptable to the
     Underwriters' counsel, familiar with the applicable laws; (B) as to matters
     of fact, to the extent such counsel deems proper, on certificates of
     responsible officers of the Company and certificates or other written
     statements of officials of jurisdictions having custody of documents
     respecting the corporate existence or good standing of the Company.  The
     opinion of such counsel for the Company shall state that the opinion of any
     such other counsel upon which they relied is in form satisfactory to such
     counsel and, in such counsel's opinion, the Underwriters and they are
     justified in relying thereon.  

                                      -19-
<PAGE>
 
     With respect to the matters to be covered in subparagraphs (ix) and (xiii)
     above counsel may state their opinion and belief is based upon their
     participation in the preparation of the Registration Statement and the
     Prospectus and any amendment or supplement thereto (other than the
     documents incorporated by reference therein) and review and discussion of
     the contents thereof (including the documents incorporated by reference
     therein) but is without independent check or verification except as
     specified.

          The opinion of Butler & Binion, L.L.P. described above shall be
     rendered to the Underwriters at the request of the Company and shall so
     state therein.

          (g)  Paul, Weiss, Rifkind, Wharton & Garrison, counsel for the 1818
     Fund, shall have furnished to the Representatives their written opinion
     dated the Closing Date or the Additional Closing Date, as the case may be,
     in form and substance satisfactory to the Representatives, to the effect
     that:

               (i)    this Agreement has been duly authorized, executed and
          delivered by such Selling Stockholder and compliance with all of the
          provisions of this Agreement and the consummation of the transactions
          contemplated herein will not result in a breach or violation of any
          terms or provisions of, or constitute a default under, any statute,
          any indenture, mortgage, deed of trust, loan agreement or other
          agreement or instrument known to such counsel to which such Selling
          Stockholder is a party or by which such Selling Stockholder is bound
          or to which any of the property or assets of such Selling Stockholder
          is subject, or any order, rule or regulation known to such counsel of
          any court or governmental agency or body having jurisdiction over such
          Selling Stockholder or the property of such Selling Stockholder,
          except for any such breach, violation or default which would not,
          individually or in the aggregate, have a material adverse effect on
          the business, assets, or financial condition of such Selling
          Stockholder or the ability of such Selling Stockholder to consummate
          the sales of the Shares;

               (ii)   no consent, approval, authorization or order of any court
          or governmental agency or body of the U.S., State of New York or the
          Delaware Revised Uniform Limited Partnership Act is required for the
          consummation of the transactions contemplated by this Agreement in
          connection with the sale of the Shares hereunder except (A) the
          registration of the Shares under the Securities Act, (B) such as may
          be required under state or foreign securities or blue sky laws in
          connection with the purchase and distribution of such Shares by the
          Underwriters and (C) such approval of the underwriting arrangements as
          may be required under the rules of the NASD;

               (iii)  such Selling Stockholder has full right, power and
          authority to sell, assign, transfer and deliver such Shares hereunder;
          and

               (iv)   upon delivery of the Shares on behalf of the Selling
          Stockholder 

                                      -20-
<PAGE>
 
          and upon payment therefor by the Underwriters pursuant to this
          Agreement, good and valid title to the Shares to be sold by such
          Selling Stockholders, free and clear of all liens, encumbrances,
          equities or claims, will be transferred to the Underwriters to the
          extent the Underwriters have purchased such Shares in good faith and
          without notice of any such lien, encumbrance, equity or claim or any
          other adverse claim within the meaning of the Uniform Commercial Code;

          (h)  Carol A. McCoy, Associate Counsel of Torchmark Corporation, the
     parent of United, shall have furnished to the Representatives her written
     opinion dated the Closing Date or the Additional Closing Date, as the case
     may be, in form and substance satisfactory to the Representatives, to the
     effect that:

               (i)    this Agreement has been duly authorized, executed and
          delivered by such Selling Stockholder and compliance with all of the
          provisions of this Agreement and the consummation of the transactions
          contemplated herein will not result in a breach or violation of any
          terms or provisions of, or constitute a default under, any statute,
          any indenture, mortgage, deed of trust, loan agreement or other
          agreement or instrument known to such counsel to which such Selling
          Stockholder is a party or by which such Selling Stockholder is bound
          or to which any of the property or assets of such Selling Stockholder
          is subject, or any order, rule or regulation known to such counsel of
          any court or governmental agency or body having jurisdiction over such
          Selling Stockholder or the property of such Selling Stockholder,
          except for any such breach, violation or default which would not,
          individually or in the aggregate, have a material adverse effect on
          the business, assets, or financial condition of such Selling
          Stockholder or the ability of such Selling Stockholder to consummate
          the sales of the Shares;

               (ii)   no consent, approval, authorization or order of any court
          or governmental agency or body is required for the consummation of the
          transactions contemplated by this Agreement in connection with the
          sale of the Shares hereunder except such as have been obtained under
          the Securities Act and such as may be required under state or foreign
          securities or blue sky laws in connection with the purchase and
          distribution of such Shares by the Underwriter and such approval of
          the underwriting arrangements as may be required under the rules of
          the NASD;

               (iii)  such Selling Stockholder has full right, power and
          authority to sell, assign, transfer and deliver such Shares hereunder;
          and

               (iv)   upon delivery of the Shares on behalf of the Selling
          Stockholder and upon payment therefor by the Underwriters pursuant to
          the Underwriting Agreement, good and valid title to the Shares to be
          sold by such Selling Stockholders, free and clear of all liens,
          encumbrances, equities or claims, will be transferred to the
          Underwriters to the extent the Underwriters have purchased such 

                                      -21-
<PAGE>
 
          Shares in good faith and without notice of any such lien, encumbrance,
          equity or claim or any other adverse claim within the meaning of the
          Uniform Commercial Code;

          (i)  on the date of the Prospectus and the effective date of the most
     recently filed post-effective amendment to the Registration Statement and
     also on the Closing Date or Additional Closing Date, as the case may be,
     KPMG Peat Marwick LLP shall have furnished to the Representatives letters,
     dated the respective dates of delivery thereof, in form and substance
     satisfactory to the Representatives, containing statements and information
     of the type customarily included in accountants' "comfort letters" to
     underwriters with respect to the financial statements and certain financial
     information contained in the Registration Statement and the Prospectus;

          (j)  the Representatives shall have received on and as of the Closing
     Date or Additional Closing Date, as the case may be, an opinion of Vinson &
     Elkins L.L.P., counsel to the Underwriters, with respect to the
     Registration Statement, the Prospectus and other related matters as the
     Representatives may reasonably request, and such counsel shall have
     received such papers and information as they may reasonably request to
     enable them to pass upon such matters;

          (k)  the Shares to be delivered on the Closing Date or Additional
     Closing Date, as the case may be, shall be listed on the New York Stock
     Exchange;

          (l)  on or prior to the Closing Date or Additional Closing Date, as
     the case may be, the Company shall have furnished to the Representatives
     such further certificates and documents as the Representatives shall
     reasonably request; and

          (m)  The "lock-up" agreements, each substantially in the form of
     Exhibit A hereto, between the Representatives and certain executive
     officers and directors of the Company relating to sales and certain other
     dispositions of shares of Stock or certain other securities, delivered to
     you on or before the date hereof, shall be in full force and effect on the
     Closing Date or Additional Closing Date, as the case may be.

     7.   The Company agrees to indemnify and hold harmless each Underwriter,
each affiliate of any Underwriter which assists such Underwriter in the
distribution of the Shares and each person, if any, who controls any Underwriter
within the meaning of either Section 15 of the Securities Act or Section 20 of
the Exchange Act, from and against any and all losses, claims, damages and
liabilities (including, without limitation, the legal fees and other expenses
incurred in connection with any suit, action or proceeding or any claim
asserted) caused by any untrue statement or alleged untrue statement of a
material fact contained in the Registration Statement or the Prospectus (as
amended or supplemented if the Company shall have furnished any amendments or
supplements thereto) or any preliminary prospectus, or caused by any omission or
alleged omission to state therein a material fact required to be stated therein
or necessary to make the statements therein not misleading, except insofar as
such losses, claims, damages or 

                                      -22-
<PAGE>
 
liabilities are caused by any untrue statement or omission or alleged untrue
statement or omission made in reliance upon and in conformity with information
relating to (a) any Underwriter furnished to the Company in writing by such
Underwriter through the Representatives or (b) any Selling Stockholder furnished
to the Company in writing by such Selling Stockholder, in either case expressly
for use therein; provided, that if any preliminary prospectus or the Prospectus
contained any alleged untrue statement of a material fact or allegedly omitted
to state therein a material fact required to be stated therein or necessary to
make the statements therein, in light of the circumstances under which they were
made, not misleading and such statement or omission shall have been corrected in
a revised preliminary prospectus or in the Prospectus (as amended or
supplemented), the Company shall not be liable to any Underwriter pursuant to
this paragraph with respect to such alleged untrue statement or alleged omission
to the extent that any such loss, claim, damage or liability of such Underwriter
results from the fact that such Underwriter sold Shares to a person to whom
there was not sent or given, at or prior to the written confirmation of such
sale, a copy of the revised preliminary prospectus or the Prospectus as so
amended or supplemented, as the case may be, containing a correction that cures
such alleged misstatement or omission, if the Company has timely provided copies
of such corrected preliminary prospectus or Prospectus to the Underwriters in
accordance with Section 5(b) hereof.

     Each Selling Stockholder agrees to indemnify and hold harmless each
Underwriter, each affiliate of any Underwriter which assists such Underwriter in
the distribution of the Shares and each person, if any, who controls any
Underwriter within the meaning of either Section 15 of the Securities Act or
Section 20 of the Exchange Act, from and against any and all losses, claims,
damages and liabilities (including, without limitation, the legal fees and other
expenses incurred in connection with any suit, action or proceeding or any claim
asserted) caused by any untrue statement or alleged untrue statement of a
material fact contained in the Registration Statement or the Prospectus (as
amended or supplemented if the Company shall have furnished any amendments or
supplements thereto) or any preliminary prospectus, or caused by any omission or
alleged omission to state therein a material fact required to be stated therein
or necessary to make the statements therein not misleading, in each case to the
extent, but only to the extent, that such untrue statement or alleged untrue
statement or omission or alleged omission was made in any preliminary
prospectus, the Registration Statement or the Prospectus or any such amendment
or supplement in reliance upon and in conformity with written information
furnished to the Company by such Selling Stockholder expressly for use therein.
Notwithstanding the foregoing, in no event shall such Selling Stockholder be
required to pay an amount in indemnification under this paragraph 7 in excess of
the net proceeds before deducting expenses at which the Shares sold by such
Selling Stockholder were offered to the public.

     Each Underwriter agrees, severally and not jointly, to indemnify and hold
harmless the Company, its directors, its officers who sign the Registration
Statement and each person who controls the Company within the meaning of Section
15 of the Securities Act and Section 20 of the Exchange Act and each Selling
Stockholder to the same extent as the foregoing indemnity from the Company to
each Underwriter, but only with reference to information relating to such
Underwriter furnished to the Company in writing by such Underwriter through the
Representatives expressly for use in the Registration Statement, the Prospectus,
any amendment 

                                      -23-
<PAGE>
 
or supplement thereto, or any preliminary prospectus.

     If any suit, action, proceeding (including any governmental or regulatory
investigation), claim or demand shall be brought or asserted against any person
in respect of which indemnity may be sought pursuant to any of the three
preceding paragraphs, such person (the "Indemnified Person") shall promptly
notify the person against whom such indemnity may be sought (the "Indemnifying
Person") in writing, and the Indemnifying Person, upon request of the
Indemnified Person, shall retain counsel reasonably satisfactory to the
Indemnified Person to represent the Indemnified Person and any others the
Indemnifying Person may designate in such proceeding and shall pay the fees and
expenses of such counsel related to such proceeding.  In any such proceed ing,
any Indemnified Person shall have the right to retain its own counsel, but the
fees and expenses of such counsel shall be at the expense of such Indemnified
Person unless (i) the Indemnifying Person and the Indemnified Person shall have
mutually agreed to the contrary, (ii) the Indemnifying Person has failed within
a reasonable time to retain counsel reasonably satisfactory to the Indemnified
Person or (iii) the named parties in any such proceeding (including any
impleaded parties) include both the Indemnifying Person and the Indemnified
Person and representation of both parties by the same counsel would be
inappropriate due to actual or potential differing interests between them.  It
is understood that the Indemnifying Person shall not, in connection with any
proceeding or related proceeding in the same jurisdiction, be liable for the
fees and expenses of more than one separate firm (in addition to any local
counsel) for all Indemnified Persons, and that all such fees and expenses shall
be reimbursed as they are incurred.  Any such separate firm for the Underwriters
and such control persons of Underwriters shall be designated in writing by J.P.
Morgan Securities Inc.  Any such separate firm for the Company, its directors,
its officers who sign the Registration Statement and such control persons of the
Company and for the Selling Stockholders shall be designated in writing by the
Company.  The Indemnifying Person shall not be liable for any settlement of any
proceeding effected without its written consent, but if settled with such
consent or if there be a final judgment for the plaintiff, the Indemnifying
Person agrees to indemnify any Indemnified Person from and against any loss or
liability by reason of such settlement or judgment.  Notwithstanding the
foregoing sentence, if at any time an Indemnified Person shall have requested an
Indemnifying Person to reimburse the Indemnified Person for fees and expenses of
counsel as contemplated by the second and third sentences of this paragraph, the
Indemnifying Person agrees that it shall be liable for any settlement of any
proceeding effected without its written consent if (i) such settlement is
entered into more than 30 days after receipt by such Indemnifying Person of the
aforesaid request and (ii) such Indemnifying Person shall not have reimbursed
the Indemnified Person in accordance with such request prior to the date of such
settlement.  No Indemnifying Person shall, without the prior written consent of
the Indemnified Person, effect any settlement of any pending or threatened
proceeding in respect of which any Indemnified Person is or could have been a
party and indemnity could have been sought hereunder by such Indemnified Person,
unless such settlement includes an unconditional release of such Indemnified
Person from all liability on claims that are the subject matter of such
proceeding.

     If the indemnification provided for in the first, second or third
paragraphs of this Section 

                                      -24-
<PAGE>
 
7 is unavailable to an Indemnified Person in respect of any losses, claims,
damages or liabilities referred to therein, then each Indemnifying Person under
such paragraph, in lieu of indemnifying such Indemnified Person thereunder,
shall contribute to the amount paid or payable by such Indemnified Person as a
result of such losses, claims, damages or liabilities (i) in such proportion as
is appropriate to reflect the relative benefits received by the Company and the
Selling Stockholders on the one hand and the Underwriters on the other hand from
the offering of the Shares or (ii) if the allocation provided by clause (i)
above is not permitted by applicable law, in such proportion as is appropriate
to reflect not only the relative benefits referred to in clause (i) above but
also the relative fault of the Company and the Selling Stockholders on the one
hand and the Underwriters on the other in connection with the statements or
omissions that resulted in such losses, claims, damages or liabilities, as well
as any other relevant equitable considerations. The relative benefits received
by the Company and the Selling Stockholders on the one hand and the Underwriters
on the other shall be deemed to be in the same respective proportions as the net
proceeds from the offering (before deducting expenses) received by the Selling
Stockholders and the total underwriting discounts and the commissions received
by the Underwriters, in each case as set forth in the table on the cover of the
Prospectus, bear to the aggregate public offering price of the Shares. The
relative fault of the Company and the Selling Stockholders on the one hand and
the Underwriters on the other shall be determined by reference to, among other
things, whether the untrue or alleged untrue statement of a material fact or the
omission or alleged omission to state a material fact relates to information
supplied by the Company or the Selling Stockholders or by the Underwriters and
the parties' relative intent, knowledge, access to information and opportunity
to correct or prevent such statement or omission.

     The Company, the Selling Stockholders and the Underwriters agree that it
would not be just and equitable if contribution pursuant to this Section 7 were
determined by pro rata allocation (even if the Underwriters were treated as one
entity for such purposes) or by any other method of allocation that does not
take account of the equitable considerations referred to in the immediately
preceding paragraph.  The amount paid or payable by an Indemnified Person as a
result of the losses, claims, damages and liabilities referred to in the
immediately preceding paragraph shall be deemed to include, subject to the
limitations set forth above, any legal or other expenses incurred by such
Indemnified Person in connection with investigating or defending any such action
or claim.  Notwithstanding the provisions of this Section 7, in no event shall
an Underwriter be required to contribute any amount in excess of the amount by
which the total price at which the Shares underwritten by it and distributed to
the public were offered to the public exceeds the amount of any damages that
such Underwriter has otherwise been required to pay by reason of such untrue or
alleged untrue statement or omission or alleged omission.  No person guilty of
fraudulent misrepresentation (within the meaning of Section ll(f) of the
Securities Act) shall be entitled to contribution from any person who was not
guilty of such fraudulent misrepresentation.  The Underwriters' obligations to
contribute pursuant to this Section 7 are several in proportion to the
respective number of Shares set forth opposite their names in Schedule I hereto,
and not joint.

     The remedies provided for in this Section 7 are not exclusive and shall not
limit any rights or remedies which may otherwise be available to any indemnified
party at law or in equity.

                                      -25-
<PAGE>
 
     The indemnity and contribution agreements contained in this Section 7 and
the representations and warranties of the Company and the Selling Stockholders
set forth in this Agreement shall remain operative and in full force and effect
regardless of (i) any termination of this Agreement, (ii) any investigation made
by or on behalf of any Underwriter or any person controlling any Underwriter or
by or on behalf of the Company, its officers or directors or any other person
controlling the Company and the Selling Stockholders and (iii) acceptance of and
payment for any of the Shares.

     8.   Notwithstanding anything herein contained, this Agreement (or the
obligations of the several Underwriters with respect to the Option Shares) may
be terminated in the absolute discretion of the Representatives, by notice given
to the Company and the Selling Stockholders, if after the execution and delivery
of this Agreement and prior to the Closing Date (or, in the case of the Option
Shares, prior to the Additional Closing Date) (i) trading generally shall have
been suspended or materially limited on or by, as the case may be, any of the
New York Stock Exchange or the American Stock Exchange, the National Association
of Securities Dealers, Inc., the Chicago Board Options Exchange, the Chicago
Mercantile Exchange or the Chicago Board of Trade, (ii) trading of any
securities of or guaranteed by the Company shall have been suspended on any
exchange or in any over-the-counter market, (iii) a general moratorium on
commercial banking activities in New York shall have been declared by either
federal or New York State authorities, or (iv) there shall have occurred any
outbreak or escalation of hostilities or any change in financial markets or any
calamity or crisis that, in the judgment of the Representatives, is material and
adverse and which, in the judgment of the Representatives, makes it
impracticable to market the Shares being delivered at the Closing Date or the
Additional Closing Date, as the case may be, on the terms and in the manner
contemplated in the Prospectus.

     9.   This Agreement shall become effective upon the later of (x) execution
and delivery hereof by the parties hereto and (y) release of notification of the
effectiveness of any post-effective amendment to the Registration Statement by
the Commission.

     If on the Closing Date or the Additional Closing Date, as the case may be,
any one or more of the Underwriters shall fail or refuse to purchase Shares
which it or they have agreed to purchase hereunder on such date, and the
aggregate number of Shares which such defaulting Underwriter or Underwriters
agreed but failed or refused to purchase is not more than one-tenth of the
aggregate number of Shares to be purchased on such date, the other Underwriters
shall be obligated severally in the proportions that the number of Shares set
forth opposite their respective names in Schedule I bears to the aggregate
number of Underwritten Shares set forth opposite the names of all such non-
defaulting Underwriters, or in such other proportions as the Representatives may
specify, to purchase the Shares which such defaulting Underwriter or
Underwriters agreed but failed or refused to purchase on such date; provided
that in no event shall the number of Shares that any Underwriter has agreed to
purchase pursuant to Section 1 be increased pursuant to this Section 9 by an
amount in excess of one-ninth of such number of Shares without the written
consent of such Underwriter.  If on the Closing Date or the Additional Closing
Date, as the case may be, any Underwriter or Underwriters shall fail or refuse
to 

                                      -26-
<PAGE>
 
purchase Shares which it or they have agreed to purchase hereunder on such date,
and the aggregate number of Shares with respect to which such default occurs is
more than one-tenth of the aggre gate number of Shares to be purchased on such
date, and arrangements satisfactory to the Representatives, the Company and the
Selling Stockholders for the purchase of such Shares are not made within 36
hours after such default, this Agreement (or the obligations of the several
Underwriters to purchase the Option Shares, as the case may be) shall terminate
without liability on the part of any non-defaulting Underwriter, the Company or
any Selling Stockholder. In any such case either you or the Selling Stockholders
shall have the right to postpone the Closing Date (or, in the case of the Option
Shares, the Additional Closing Date), but in no event for longer than seven
days, in order that the required changes, if any, in the Registration Statement
and in the Prospectus or in any other documents or arrangements may be effected.
Any action taken under this paragraph shall not relieve any defaulting
Underwriter from liability in respect of any default of such Underwriter under
this Agreement.

     10.  If this Agreement shall be terminated by the Underwriters, or any of
them, because of any failure or refusal on the part of the Company to comply
with the terms or to fulfill any of the conditions of this Agreement, or if for
any reason the Company or the Selling Stockholders shall be unable to perform
their respective obligations under this Agreement or any condition of the
Underwriters' obligations cannot be fulfilled, the Company agrees to reimburse
the Under writers or such Underwriters as have so terminated this Agreement with
respect to themselves, severally, for all out-of-pocket expenses (including the
fees and expenses of its counsel) reason ably incurred by the Underwriter in
connection with this Agreement or the offering contemplated hereunder.

     11.  This Agreement shall inure to the benefit of and be binding upon the
Company, the Underwriters and the Selling Stockholders, any controlling persons
of the Company referred to herein and their respective successors and assigns.
Nothing expressed or mentioned in this Agreement is intended or shall be
construed to give any other person, firm or corporation any legal or equitable
right, remedy or claim under or in respect of this Agreement or any provision
herein contained.  No purchaser of Shares from any Underwriter shall be deemed
to be a successor by reason merely of such purchase.

     12.  Any action by the Underwriters hereunder may be taken by the
Representatives jointly or by J.P. Morgan Securities Inc. alone on behalf of the
Underwriters, and any such action taken by the Representatives jointly or by
J.P. Morgan Securities Inc. alone shall be binding upon the Underwriters.  All
notices and other communications hereunder shall be in writing and shall be
deemed to have been duly given if mailed or transmitted by any standard form of
telecommunication. Notices to the Underwriters shall be given to the
Representatives, c/o J.P. Morgan Securities Inc., 60 Wall Street, New York, New
York 10260 (telefax: (212) 648-5705); Attention: Syndicate Department.  Notices
to the Company shall be given to it at 1331 Lamar, Suite 1650, Houston, Texas
77010 (telefax: (713) 756-1744), Attention: Michael D. Watford.  Notices to The
1818 Fund, L.P. shall be given to it at c/o Brown Brothers Harriman, 59 Wall
Street, New York, New York 10005 (telefax: (212) 493-8429), Attention: Walter
Grist, and notices to United Investors Management Company shall be given to it
at c/o Torchmark 

                                      -27-
<PAGE>
 
Corporation, 2001 Third Avenue, South, Birmingham, Alabama 85233 (telefax: (205)
325-4198), Attention: Duncan Hamilton.

                                      -28-
<PAGE>
 
     13.  This Agreement may be signed in counterparts, each of which shall be
an original and all of which together shall constitute one and the same
instrument.

     14.  THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH
THE LAWS OF THE STATE OF NEW YORK, WITHOUT GIVING EFFECT TO THE CONFLICTS OF
LAWS PROVISIONS THEREOF.

     If the foregoing is in accordance with your understanding, please sign and
return four counterparts hereof.

                              Very truly yours,

                              NUEVO ENERGY COMPANY


                              By: /s/ Michael D. Watford
                                  ----------------------
                                  Name:   Michael D. Watford
                                  Title:  President & Chief Executive Officer


                              THE SELLING STOCKHOLDERS:

                              THE 1818 FUND, L.P.


                              By: /s/ Lawrence C. Tucker
                                  ----------------------
                                  Name:   Lawrence C. Tucker
                                  Title:  Partner, Brown Brothers Harriman & Co.
                                          as General Partner of The 1818 Fund,
                                          L.P.


                              UNITED INVESTORS MANAGEMENT
                                COMPANY


                              By: /s/ Carol A. McCoy
                                  ------------------
                                  Name:   Carol A. McCoy
                                  Title:  Assistant Secretary

                                      -29-
<PAGE>
 
Accepted:  December 18, 1996

J.P. MORGAN SECURITIES INC.
DONALDSON, LUFKIN & JENRETTE
 SECURITIES CORPORATION
MORGAN KEEGAN & COMPANY, INC.
PAINEWEBBER INCORPORATED

Acting severally on behalf of themselves
 and the several Underwriters listed in
 Schedule I hereto

By:  J.P. MORGAN SECURITIES INC.
     Acting on behalf of itself and the
      several Underwriters listed in
      Schedule I hereto

     By: /s/ Ferrell P. McLean
         ----------------------------
         Name:  Ferrell P. McClean
         Title: Managing Director

                                      -30-
<PAGE>
 
                                  SCHEDULE I

<TABLE>
<CAPTION>
-----------                               -------------------   
UNDERWRITER                                    NUMBER OF
                                          UNDERWRITTEN SHARES
                                            TO BE PURCHASED
<S>                                       <C>
J.P. Morgan Securities Inc..............              340,000
Donaldson, Lufkin & Jenrette Securities               340,000
Corporation.............................
Morgan Keegan & Company, Inc............              340,000
PaineWebber Incorporated................              340,000
BT Securities Corporation...............               50,000
A.G. Edwards & Sons, Inc................               50,000
Lehman Brothers Inc.....................               50,000
Smith Barney Inc........................               50,000
Howard, Weil, Labouisse, Friedrichs Inc.               50,000
Jefferies & Company, Inc................               50,000
Johnson Rice & Company L.L.C............               50,000
Petrie Parkman & Co., Inc...............               50,000
Principal Financial Securities, Inc.....               50,000
Rauscher Pierce Refsnes, Inc............               50,000
                                          -------------------
          Total.........................            1,860,000
                                          ===================
</TABLE>
<PAGE>
 
                                  SCHEDULE II

<TABLE> 
<CAPTION> 
-------------------                                              ------------ 
SELLING STOCKHOLDER                                               NUMBER OF  
                                                                 UNDERWRITTEN
                                                                 SHARES TO BE
                                                                     SOLD    
<S>                                                              <C>         
United Investors Management Company............................     1,171,395
The 1818 Fund, L.P.............................................       688,605
                                                                    ---------
                                                                             
          Total................................................     1,860,000
--------------------------------------------------------------------========= 
</TABLE>
<PAGE>
 
                                                                       EXHIBIT A
                                                                       ---------

                               LOCK-UP AGREEMENT


                               December ___, 1996


J.P. Morgan Securities Inc.
Donaldson, Lufkin & Jenrette Securities Corporation
Morgan Keegan & Company, Inc.
PaineWebber Incorporated
As Representatives of the several Underwriters
c/o J.P. Morgan Securities Inc.
60 Wall Street
New York, New York  10260

J.P. Morgan Securities Inc.
Salomon Brothers Inc
c/o J.P. Morgan Securities Inc.
60 Wall Street
New York, New York  10260

Dear Ladies and Gentlemen:

     The undersigned understands that certain of you propose to enter into (i)
an Underwriting Agreement (the "TECONS Underwriting Agreement") with Nuevo
Financing I, a statutory business trust created under the laws of the State of
Delaware (the "Trust") and Nuevo Energy Company, a Delaware corporation (the
"Company"), providing for the public offering (the "TECONS Public Offering") by
you of 2,000,000 of the Trust's $_____ Term Convertible Securities, Series A and
up to an additional 300,000 of the Trust's $_____ Term Convertible Securities,
Series A, solely to cover over-allotments (collectively, the "TECONS") and (ii)
an Underwriting Agreement (the "Common Stock Underwriting Agreement" and,
together with the TECONS Underwriting Agreement, the "Underwriting Agreements")
with the Company, The 1818 Fund, L.P. and United Investors Management Company
(the "Selling Stockholders") providing for the public offering (the "Common
Stock Public Offering" and, together with the TECONS Public Offering, the
"Public Offerings") by you of 1,860,000 shares of the common stock $.01 par
value, of the Company (the "Nuevo Common Stock"), and up to an aggregate of
278,605 additional shares of Common Stock, solely to cover over-allotments.
Capitalized terms used herein and not otherwise defined shall have the meanings
set forth in the Underwriting Agreements.

     In consideration of your agreement to purchase and make the Public
Offerings, and for other good and valuable consideration receipt of which is
hereby acknowledged, the undersigned 

                                      A-1
<PAGE>
 
hereby agrees that, without the prior written consent of J.P. Morgan Securities
Inc. on your behalf, the undersigned will not, during the period ending 90 days
after the date of the prospectus supplement relating either to the TECONS or the
Common Stock (the "Prospectus"), (1) offer, pledge to sell, file a registration
statement relating to, announce the intention to sell, sell, issue, contract to
sell, sell any option or contract to purchase, purchase any option or contract
to sell, grant any option, right or warrant to purchase, or otherwise transfer
or dispose of, directly or indirectly, any Nuevo Common Stock or any securities
convertible into or exercisable or exchangeable for Nuevo Common Stock
(including, without limitation, Nuevo Common Stock which may be deemed to be
beneficially owned by the undersigned in accordance with the rules and
regulations of the Securities and Exchange Commission and securities which may
be issued upon exercise of a stock option or warrant), or (2) enter into any
swap or other agreement that transfers, in whole or in part, any of the economic
consequences of ownership of the Nuevo Common Stock, whether any such
transaction described in clause (1) or (2) above is to be settled by delivery of
Nuevo Common Stock or such other securities, in cash or otherwise.

     Notwithstanding the preceding paragraph, this lock-up agreement shall not
prohibit any transfer or other disposition by the undersigned involving any of
the following:  (1) a transfer or disposition of shares of Nuevo Common Stock to
his or her spouse, siblings, parents or any natural or adopted children or other
descendants or to any personal trust in which such family members or the
undersigned retains the entire beneficial interest; (2) a transfer or
disposition of shares of Nuevo Common Stock on his or her death to the
undersigned's estate, executor, administrator or personal representative or to
the undersigned's beneficiaries pursuant to a devise or bequest or by the laws
of descent and distribution; (3) a transfer or disposition of shares of Nuevo
Common Stock as a bona fide gift; and (4) a pledge of Nuevo Common Stock as
collateral, to a banking institution; provided, in each case, that the
transferee, pledgee or other person receiving such shares shall agree to all of
the restrictions set forth in this lock-up agreement.

     The undersigned hereby represents and warrants that the undersigned has
full power and authority to enter into this lock-up agreement, and that, upon
request, the undersigned will execute any additional documents necessary or
desirable in connection with the enforcement hereof.  All authority herein
conferred to or agreed to be conferred and any obligations of the undersigned
shall be binding upon the successors and assigns of the undersigned.

     In furtherance of the foregoing, the Company, the Trust, and any duly
appointed transfer agent for the registration or transfer of the securities
described herein, are hereby authorized to decline to make any transfer of
securities if such transfer would constitute a violation or breach of this lock-
up agreement.

     The undersigned understands that, if both Underwriting Agreements do not
become effective, or if both Underwriting Agreements (other than the provisions
thereof which survive termination) shall terminate or be terminated prior to
payment for and delivery of the TECONS and the Common Stock, the undersigned
shall be released from all obligations to you under this lock-up agreement.

                                      A-2
<PAGE>
 
     This lock-up agreement shall be governed by and construed in accordance
with the laws of the State of New York, without regard to the conflict of laws
principles thereof.

     The undersigned understands that the Underwriters are entering into the
Underwriting Agreements and proceeding with the Public Offerings in reliance
upon this letter agreement.  The undersigned agrees that the provisions of this
letter agreement shall also be binding upon the successors, assigns, heirs or
personal representatives of the undersigned, as the case may be.

                                    Very truly yours,



                                    By_________________________________
                                      Name:
                                      Title:

Accepted as of the date first set forth above:

J.P. MORGAN SECURITIES INC.
DONALDSON, LUFKIN & JENRETTE
 SECURITIES CORPORATION
MORGAN KEEGAN & COMPANY, INC.
PAINEWEBBER INCORPORATED

Acting severally on behalf of themselves
 and the several Underwriters

By:  J.P. MORGAN SECURITIES INC.
     Acting on behalf of itself and the
      several Underwriters

     By:__________________________
        Name:
        Title:

J.P. MORGAN SECURITIES INC.
SALOMON BROTHERS INC

By:  J.P. MORGAN SECURITIES INC.
     Acting on behalf of itself and the
      several Underwriters

     By:____________________________

                                      A-3
<PAGE>
 
        Name:
        Title:

                                      A-4