<PAGE>
 
                                                                     EXHIBIT 1.2

                            UNDERWRITING AGREEMENT

                               NUEVO FINANCING I


                     2,000,000 TRUST PREFERRED SECURITIES



                                                               December 18, 1996


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

Ladies and Gentlemen:

     Nuevo Financing I, a statutory business trust created under the laws of the
State of Delaware (the "Trust"), proposes to issue and sell to the several
Underwriters listed in Schedule I hereto (the "Underwriters") an aggregate of
2,000,000 of its $2.875 Term Convertible Securities, Series A (the "Underwritten
Trust Preferred Securities") and, for the sole purpose of covering over-
allotments in connection with the sale of the Underwritten Trust Preferred
Securities, up to an additional 300,000 of its $2.875 Term Convertible
Securities, Series A (the "Option Trust Preferred Securities").  The
Underwritten Trust Preferred Securities and the Option Trust Preferred
Securities are herein referred to as the "Trust Preferred Securities."

     The Trust Preferred Securities will be guaranteed (the "Guarantee") by
Nuevo Energy Company, a Delaware corporation (the "Company"), to the extent
described in a Preferred Securities Guarantee Agreement to be dated as of the
Closing Date and will be convertible into the common shares, $.01 par value, of
the Company ("Nuevo Common Stock").  The Company will also be the holder of one
hundred percent of the common securities representing undivided beneficial
interests in the assets of the Trust (the "Trust Common Securities," and
together with the Trust Preferred Securities, the "Trust Securities").  The
Trust will use the proceeds from the sale of the Trust Securities to purchase
from the Company an equal aggregate principal amount of its 5.75% Convertible
Subordinated Debentures due December 15, 2026 (the "Convertible Debentures") to
be issued under a subordinated debenture (the "Base Indenture") dated as of
November 25, 1996 between the Company and Wilmington Trust Company, as trustee
(the "Indenture Trustee"), as supplemented by the First Supplemental Indenture
to be dated as of the Closing Date (the "Supplemental Indenture," and together
with the Base Indenture, the "Indenture").  The Trust has been created and
continued under Delaware law pursuant to an Amended and Restated Declaration of
Trust (the "Declaration") to be executed by the Company 
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and by the trustees of the Trust (the "Nuevo Trustees"), all of whom have been
appointed by the Company, as holder of one hundred percent of the Trust Common
Securities. A majority of the Nuevo Trustees (the "Regular Trustees") are
persons who are employees or officers of or affiliated with the Company. One
Nuevo Trustee, Wilmington Trust Company, is unaffiliated with the Company and
shall act as institutional trustee ("Institutional Trustee") and as Indenture
Trustee for the purposes of the Trust Indenture Act of 1939 (the "Trust
Indenture Act").

     The Company and the Trust have 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 Trust Preferred
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 Trust Preferred Securities, in the
form first used to confirm sales of Securities 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 "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.

     Each of the Trust and the Company hereby agree with the Underwriters as
follows:

     1.   The Trust agrees to issue and sell the Underwritten Trust Preferred
Securities to the several Underwriters as hereinafter provided, and each
Underwriter, upon the basis of the representations and warranties of the Trust
and the Company herein contained, but subject to the conditions hereinafter
stated, agrees to purchase, severally and not jointly, from the Trust the
respective number of Underwritten Trust Preferred Securities set forth opposite
such Underwriter's name in Schedule I hereto, at a purchase price per
Underwritten Trust Preferred Security (the "Purchase Price") of $50.00.

     In addition, the Trust agrees to issue and sell the Option Trust Preferred
Securities to the several Underwriters as hereinafter provided, and each
Underwriter, on the basis of the representations and warranties of the Trust and
the Company herein contained, but subject to the conditions hereinafter stated,
shall have the option to purchase, severally and not jointly, from 

                                      -2-
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the Trust up to an aggregate of 300,000 Option Trust Preferred Securities at the
Purchase Price plus accumulated Distributions, if any, from December 23, 1996,
for the sole purpose of covering over-allotments (if any) in the sale of the
Underwritten Trust Preferred Securities by the several Underwriters.

     If the Option Trust Preferred Securities are to be purchased, the number of
Option Trust Preferred Securities to be purchased by each Underwriter shall be
the number of Option Trust Preferred Securities which bears the same ratio to
the aggregate number of Option Trust Preferred Securities being purchased as the
number of Underwritten Trust Preferred Securities set forth opposite the name of
such Underwriter in Schedule I hereto bears to the aggregate number of
Underwritten Trust Preferred Securities being purchased from the Trust by the
several Underwriters, subject, however, to such adjustments to eliminate any
fractional Trust Preferred Securities as the Underwriters in their sole
discretion shall make.

     The Underwriters may exercise the option to purchase the Option Trust
Preferred Securities at any time (but not more than once) on or before the
thirtieth day following the date of this Agreement, by written notice from the
Underwriters to the Trust.  Such notice shall set forth the aggregate number of
Option Trust Preferred Securities as to which the Option is being exercised and
the date and time when the Option Trust Preferred Securities 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.  Any such notice shall be given at least two Business Days prior to the
date and time of delivery specified therein.

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

     3.   Payment for the Trust Preferred Securities shall be made by wire
transfer in immediately available funds, to the account specified by the Trust
to the Underwriters no later than noon the Business Day (as defined below) prior
to the Closing Date (as defined below), in the case of the Underwritten Trust
Preferred Securities, 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
Underwriters and the Trust may agree upon in writing or, in the case of the
Option Trust Preferred Securities, on the date and time specified by the
Underwriters in the written notice of the Underwriters' election to purchase
such Option Trust Preferred Securities.  The time and date of such payment for
the Underwritten Trust Preferred Securities is referred to herein as the
"Closing Date," and the time and date of such payment for the Option Trust
Preferred Securities, if other than the Closing Date, is referred to herein 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 Trust Preferred Securities to be purchased on the Closing
Date or the 

                                      -3-
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Additional Closing Date, as the case may be, shall be made against delivery to
the Underwriters for the respective accounts of the several Underwriters of the
Trust Preferred Securities to be purchased on such date registered in such names
and in such denominations as the Underwriters 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 Trust Preferred Securities duly paid by the
Company. The certificates for the Trust Preferred Securities will be made
available for inspection and packaging by the Underwriters 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.

     As compensation to the Underwriters for their commitments hereunder, the
Company on the Closing Date or the Additional Closing Date, as the case may be,
will pay, or cause to be paid, to J.P. Morgan Securities Inc., for the accounts
of the several Underwriters, an amount equal to $1.375 per Trust Preferred
Security for the Trust Preferred Securities to be delivered by the Trust
hereunder on the Closing Date or the Additional Closing Date, as the case may
be.  The Company will pay or cause to be paid such commission payable to the
order of J.P. Morgan Securities Inc. in immediately available funds to the
account specified by J.P. Morgan Securities Inc. no later than noon the Business
Day prior to the Closing Date or the Additional Closing Date, as the case may
be.

     4.   Each of the Trust and the Company jointly and severally represent and
warrant to each Underwriter that:

          (a)  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 any
     Underwriter furnished to the Trust and the Company in writing by such
     Underwriter expressly for use therein;

          (b)  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 each of the Trust and the Company,
     threatened by the Commission; and the Registration Statement and Prospectus
     (as amended or supplemented if the Trust or 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 

                                      -4-
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     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, as of the date of the Prospectus and any
     amendments or supplements thereto and at the Closing Date or the Additional
     Closing Date, as the case may be, did not and 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 any Underwriter furnished to the
     Trust or the Company in writing by such Underwriter expressly for use
     therein;

          (c)  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;

          (d)  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 the Company's 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 each of the Trust and
     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 

                                      -5-
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     consistent with such financial statements and the books and records of the
     Company;

          (e)  since the respective dates as of which information is given in
     the Registration Statement and the Prospectus, there has not been any
     material change in the capital stock or long-term debt of the Company or
     any of the Company's subsidiaries, or any material adverse change, or any
     development reasonably likely to involve 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 the Company's 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;

          (f)  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 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;

          (g)  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 qualified as a foreign corporation for the transaction of business and
     is in good standing under the laws of each other jurisdiction in which its
     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 of the outstanding shares of
     capital stock of each corporate subsidiary of the Company have been duly
     authorized and validly issued, are fully paid and nonassessable and, except
     for 20%, 50% and 27.88% of the outstanding 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;

          (h)  the Trust has been duly created and is validly existing in good
     standing as a business trust under the Delaware Business Trust Act, has the
     trust power and authority to conduct its affairs as presently conducted and
     as described in the Registration Statement and the Prospectus, and is not
     required to be authorized to do business in any 

                                      -6-
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     other jurisdiction; the Trust has not conducted any business, entered into
     any agreements or incurred any debt or obligations other than the execution
     of this Agreement and the consummation of the transactions contemplated
     hereby;

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

          (j)  the Indenture has been duly qualified under the Trust Indenture
     Act and has been duly authorized, executed and delivered by the Company
     and, assuming due authorization, execution and delivery thereof by the
     Indenture Trustee, will be as of the Closing Date, a valid and binding
     agreement of the Company, enforceable in accordance with its terms, subject
     to bankruptcy, insolvency or similar laws affecting creditors' rights
     generally and by general principles of equity and public policy;

          (k)  the Declaration has been duly qualified under the Trust Indenture
     Act and has been duly authorized by the Company and, upon execution and
     delivery thereof by the Company, and assuming due authorization, execution
     and delivery thereof by the Nuevo Trustees and the Institutional Trustee,
     the Declaration will, as of the Closing Date or the Additional Closing
     Date, as the case may be, be a valid and binding agreement of the Company,
     the Nuevo Trustees and the Institutional Trustee, in each case enforceable
     in accordance with its terms, subject to bankruptcy, insolvency or similar
     laws affecting creditors' rights generally and by general principles of
     equity and public policy;

          (l)  the Guarantee has been duly qualified under the Trust Indenture
     Act and has been duly authorized by the Company, and upon execution and
     delivery thereof by the Company and assuming the due authorization,
     execution and delivery thereof by the trustee under the Guarantee, the
     Guarantee will, as of the Closing Date or the Additional Closing Date, as
     the case may be, be a valid and binding agreement of the Company,
     enforceable in accordance with its terms, subject to bankruptcy, insolvency
     or similar laws affecting creditors' rights generally and to general
     principles of equity and public policy;

          (m)  the Convertible Debentures have been duly authorized and, when
     executed by the Company, authenticated by the Indenture Trustee, issued in
     accordance with the Indenture and delivered to the Trust against payment
     therefor as described in the Registration Statement and the Prospectus,
     will constitute valid and binding obligations of the Company, enforceable
     in accordance with their terms, subject to bankruptcy, insolvency or
     similar laws affecting creditors' rights generally and to general
     principles of equity and public policy;

          (n)  the Trust Preferred Securities have been duly authorized by the
     Declaration and, when issued and delivered in accordance with the terms of
     this Agreement and the Declaration, will be validly issued undivided
     beneficial interests in the assets of the Trust, and the issuance of such
     Trust Preferred Securities will not be 

                                      -7-
<PAGE>
 
     subject to any preemptive or similar rights. The Trust Common Securities to
     be issued to the Company will be authorized by the Declaration and, when
     executed in accordance with the terms of the Declaration and delivered to
     the Company against payment therefor as described in the Registration
     Statement and the Prospectus, will represent validly issued undivided
     beneficial interests in the assets of the Trust;

          (o)  the shares of Nuevo Common Stock initially issuable upon the
     conversion of the Convertible Debentures and the Trust Preferred Securities
     have been duly authorized and reserved for issuance upon such conversion
     and, when issued upon such conversion, will be duly issued, fully paid and
     nonassessable and will not be subject to any preemptive or similar rights;

          (p)  the Company has an authorized capitalization as set forth in the
     Prospectus and the 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 nonassessable 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, preemptive 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;

          (q)  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 material to the Company and the Company's subsidiaries, taken as a
     whole; the issue and sale of the Trust Securities and the performance by
     the Company of its obligations under this Agreement, the Declaration, the
     Guarantee and the Indenture, the issuance and sale of the Convertible
     Debentures, and the conversion of the Convertible Debentures and the Trust
     Preferred Securities into Nuevo Common Stock, 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 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 

                                      -8-
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     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 issue and sale of the Trust Securities 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 Trust Securities by the Underwriters;

          (r)  the Trust is not, nor with the giving of notice or lapse of time
     or both would it be, in violation of or in default under, the Declaration
     or any other agreement or instrument to which the Trust is a party; the
     issue and sale of the Trust Preferred Securities and the performance by the
     Trust of its obligations under this Agreement, the Declaration and the
     Guarantee 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 agreement or instrument to which the
     Trust is a party or by which the Trust is bound, nor will any such action
     result in any violation of the provisions of the Declaration or any
     applicable law or statute or any order, rule or regulation of any court or
     governmental agency or body having jurisdiction over the Trust or any of
     its 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 issue and sale of the Trust Preferred
     Securities or the consummation by the Trust 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 Trust Preferred Securities by the Underwriters;

          (s)  other than as set forth or contemplated in the Prospectus, there
     are no legal or governmental investigations, actions, suits or proceeds
     pending or, to the knowledge of the Company, threatened against or
     affecting the Trust, the Company or any of its subsidiaries or any of their
     respective properties or to which the Trust, the Company or any of its
     subsidiaries is or may be a party or to which any property of the Trust,
     the Company or any of its subsidiaries is or may be the subject which, if
     determined adversely to the Trust, the Company or any of the Company's
     subsidiaries, could individually or in the aggregate reasonably be expected
     to have a material adverse effect on the Trust or 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;

          (t)  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 

                                      -9-
<PAGE>
 
     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;

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

          (v)  no person 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 Trust Securities other than the Selling Stockholders described
     in the Prospectus;

          (w)  the Trust is not, and after giving effect to the offering and
     sale of the Trust Preferred Securities and the application of the proceeds
     thereof as described in the Prospectus, will not be an "investment company"
     as such term is defined in the Investment Company Act of 1940, as amended
     (the "Investment Company Act"), and the Company is not, and after giving
     effect to the issuance of the Convertible Debentures and the application of
     the proceeds thereof as described in the Prospectus, will not be an
     "investment company" as such term is defined in the Investment Company Act;

          (x)  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");

          (y)  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;

          (z)  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;

          (aa) 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 

                                      -10-
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     or might reasonably be expected to be asserted or threatened against the
     Company or any subsidiary;

          (bb) 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
     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;

          (cc) 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;

          (dd) 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;

          (ee) 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 

                                      -11-
<PAGE>
 
     its subsidiaries, taken as a whole;
 
          (ff) 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 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;

          (gg) 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;

          (hh) 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;

          (ii) 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;

                                      -12-
<PAGE>
 
          (jj) 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;

          (kk) 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
     or in the aggregate, have a material adverse effect on the Company and its
     subsidiaries, taken as a whole;

          (ll) 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;

          (mm) 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
     Nuevo Common Stock; and

          (nn) 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.

     5.   Each of the Trust and 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 timely file 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 Trust Preferred Securities; and to furnish
     copies of the Prospectus to the 

                                      -13-
<PAGE>
 
     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 Underwriters may reasonably request;

          (b)  to deliver, at the expense of the Company, to the Underwriters
     three (3) 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 reference therein as the Underwriters may
     reasonably request;

          (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 Underwriters a
     copy of the proposed amendment or supplement for review and not to file any
     such proposed amendment or supplement to which the Underwriters reasonably
     object;

          (d)  to advise the Underwriters 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 Underwriters 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 Trust Preferred Securities 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 Trust Preferred Securities, 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 Trust Preferred Securities as in the opinion of counsel for
     the Underwriters a 

                                      -14-
<PAGE>
 
     prospectus relating to the Trust Preferred Securities 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 Underwriters will furnish to the Company) to which Trust Preferred
     Securities may have been sold by 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 Trust Preferred Securities, the
     Guarantee, the Convertible Debentures and the Nuevo Common Stock for offer
     and sale under the securities or Blue Sky laws of such jurisdictions as the
     Underwriters shall reasonably request and to continue such qualification in
     effect so long as reasonably required for distribution of the Trust
     Preferred Securities; provided that neither the Company nor the Trust shall
     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
     Underwriters as soon as practicable an earnings statement of the Company
     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 date hereof, to furnish to the
     Underwriters copies of all reports or other communications (financial or
     other) furnished to holders of the Trust Securities, 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 (x) 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 Nuevo Common Stock ("Stock") or any securities convertible into or
     exercisable or exchangeable for Stock or (y) 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 (x) or (y) above is 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 (i) the Trust may sell the Trust Preferred
     Securities to the Underwriters as contemplated hereunder, (ii) the Company
     may sell the Convertible Debentures to the Trust as contemplated hereunder,
     (iii) the Company may issue Stock upon conversion of any Convertible
     Debentures, (iv) the Company may issue Stock 

                                      -15-
<PAGE>
 
     pursuant to existing stock incentive plans, (v) the Company may issue Stock
     upon conversion of the 7% Cumulative Convertible Preferred Stock, and (vi)
     the Company may issue Stock or other rights to acquire Stock as
     consideration for acquired businesses, provided 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 list, subject to notice of issuance,
     the Trust Preferred Securities on the New York Stock Exchange (the
     "Exchange");

          (k)  to reserve and keep available at all times, free of preemptive
     rights, Nuevo Common Stock for the purpose of enabling the Company to
     satisfy any obligations to issue Nuevo Common Stock upon the conversion of
     the Convertible Debentures and the Trust Preferred Securities; and

          (l)  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 Trust Preferred Securities and the Convertible Debentures,
     including any transfer taxes payable in connection with the transfer of
     Trust Preferred Securities to the Underwriters, (ii) of the Company, its
     counsel and its accountants 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, amendments and supplements thereto), (iii) incurred in connection
     with the registration or qualification of the Trust Preferred Securities,
     the Guarantee, the Convertible Debentures and the Nuevo Common Stock under
     the laws of such jurisdictions as the Underwriters may designate (including
     reasonable fees of counsel for the Underwriters and its disbursements),
     (iv) in connection with the listing of the Trust Preferred Securities 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 security
     certificates, (viii) the cost and charges of any transfer agent and any
     registrar, (ix) the fees and expenses of the Trustee and the reasonable
     fees and disbursements of counsel for the Trustee in connection with the
     Indenture and the Convertible Debentures, and (x) the fees and expenses
     associated with obtaining ratings for the Trust Preferred Securities from
     nationally recognized statistical rating organizations.

     6.   The several obligations of the Underwriters hereunder to purchase the
Trust Preferred Securities on the Closing Date or the Additional Closing Date,
as the case may be, are subject to the performance by the Company and the Trust
of their respective obligations 

                                      -16-
<PAGE>
 
hereunder and to the following additional conditions:

          (a)  the Registration Statement shall be effective on the date hereof
     (if a post-effective amendment is required to be filed by 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 Underwriters;

          (b)  the representations and warranties of the Trust and the Company
     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
     Trust 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 or the Trust by any "nationally recognized statistical rating
     organization," as such term is defined for purposes of Rule 436(g)(2) under
     the Securities Act;

          (d)  since the respective dates as of which information is given in
     the Prospectus there shall not have been any material change in the capital
     stock or long-term debt of the Trust, the Company or any of the Company's
     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 Trust or 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 reasonable judgment of the
     Underwriters makes it impracticable or inadvisable to proceed with the
     public offering or the delivery of the Trust Preferred Securities 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
     Trust, 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

                                      -17-
<PAGE>
 
     Prospectus;

          (e)  the Underwriters shall have received on and as of the Closing
     Date or the Additional Closing Date, as the case may be, certificates of an
     executive officer of the Company and of a Regular Trustee of the Trust,
     with specific knowledge about the Company's and the Trust's financial
     matters, satisfactory to the Underwriters to the effect set forth in
     subsections 6(a) through 6(c) (with respect to the respective
     representations, warranties, agreements and conditions of the Company or
     the Trust) hereof and to the further effect that there has not occurred any
     material adverse change, or any development reasonably likely to involve a
     prospective material adverse change, in or affecting the general affairs,
     business, prospects, management financial position, stockholders' equity or
     results of operations of the Trust or the Company and its subsidiaries,
     taken as a whole, from that set forth or contemplated in the Registration
     Statement;

          (f)  Richards, Layton & Finger, special Delaware counsel for the Trust
     and the Company shall have given to the Underwriters their written opinion
     dated the Closing Date or the Additional Closing Date, as the case may be,
     in form and substance satisfactory to the Underwriters, to the effect that:

               (i)    the Trust has been duly created and is validly existing in
          good standing as a business trust under the Delaware Business Trust
          Act, and all filings required under the laws of the State of Delaware
          with respect to the creation and valid existence of the Trust as a
          business trust have been made;

               (ii)   under the Declaration and the Delaware Business Trust Act,
          the Trust has the trust power and authority (i) to own property and
          conduct its business, all as described in the Prospectus and the
          Prospectus Supplement, (ii) to issue and sell the Trust Securities in
          accordance with the Declaration, and as described in the Prospectus
          and Prospectus Supplement, and to perform its other obligations under
          the Declaration, this Agreement and the Trust Securities, (iii) to
          deliver this Agreement, and (iv) to consummate the transactions
          contemplated by this Agreement;

               (iii)  the Declaration constitutes a valid and binding obligation
          of the Company and the Nuevo Trustees, and is enforceable against the
          Company and the Nuevo Trustees, in accordance with its terms, subject
          to the effect upon the Declaration of (x) bankruptcy, insolvency,
          moratorium, receivership, reorganization, liquidation, fraudulent
          conveyance or transfer and other similar laws relating to or affecting
          the rights and remedies of creditors generally, (y) principles of
          equity, including applicable law relating to fiduciary duties
          (regardless of whether considered and applied in a proceeding in
          equity or at law), and (z) the effect of applicable public policy on
          the enforceability of provisions relating to indemnification or
          contribution;

                                      -18-
<PAGE>
 
               (iv)  the Trust Common Securities have been authorized by the
          Declaration and are duly and validly issued and undivided beneficial
          interests in the assets of the Trust;

               (v)   the Trust Preferred Securities have been duly authorized by
          the Declaration and are duly and validly issued and, subject to the
          qualifications set forth in paragraph 6(f)(vi) below, fully paid and
          nonassessable undivided beneficial interests in the assets of the
          Trust;

               (vi)  the holders of the Trust Preferred Securities, as
          beneficial owners of the Trust will be entitled to the same limitation
          of personal liability extended to stockholders of private corporations
          for profit organized under the General Corporation Law of the State of
          Delaware; provided that the holders of Trust Preferred Securities may
          be obligated, pursuant to the Declaration, (i) to provide indemnity
          and/or security in connection with and pay taxes or governmental
          charges arising from transfers or exchanges of Trust Preferred
          Securities Certificates and the issuance of replacement Trust
          Preferred Securities Certificates, and (ii) to provide security or
          indemnity in connection with requests of or directions to the
          Institutional Trustee to exercise its rights and powers under the
          Declaration;

               (vii)  under the Declaration and the Delaware Business Trust Act,
          the issuance of the Trust Securities is not subject to preemptive
          rights;

               (viii)  the issuance and sale by the Trust of the Trust
          Securities and the delivery and performance by the Trust and the
          consummation of the transactions contemplated by this Agreement do not
          violate (i) the Declaration, or (ii) any applicable Delaware law, rule
          or regulation;

               (ix)  under the Declaration and the Delaware Business Trust Act,
          (i) issuance and sale by the trust of the Trust Securities and the
          delivery by the Trust of this Agreement, and the performance by the
          Trust of its obligations hereunder, have been duly authorized by all
          necessary trust action on the part of the Trust, and (ii) assuming the
          due authorization, execution and delivery of (x) this Agreement by the
          Company as depositor under the Declaration on behalf of the Trust, and
          (y) the Trust Preferred Securities Certificates for the Trust
          Preferred Securities by a Regular Trustee on behalf of the Trust and
          assuming the due authentication of the Trust Preferred Securities
          Certificates by the Institutional Trustee, this Agreement has been
          duly delivered by the Trust and the Trust Preferred Securities
          Certificates have been duly executed and delivered by the Trust;

               (x)  no authorization, approval, consent or order of any Delaware
          court

                       

                                      -19-
<PAGE>
 
          or Delaware governmental authority or Delaware agency is required to
          be obtained by the Trust solely as a result of the issuance and sale
          of the Trust Preferred Securities, the consummation by the Trust of
          the transactions contemplated by this Agreement or the compliance by
          the Trust of its obligations under this Agreement;

               (xi)  the holders of Trust Preferred Securities (other than those
          holders who reside or are domiciled in the State of Delaware) will
          have no liability for income taxes imposed by the State of Delaware
          solely as a result of their participation in the Trust, and the Trust
          will not be liable for any income tax imposed by the State of
          Delaware; and

               (xii)  after due inquiry on December ___, 1996, limited to, and
          solely to the extent disclosed thereupon, court dockets for active
          cases of the Court of Chancery of the State of Delaware in and for New
          Castle County, Delaware, of the Superior Court of the State of
          Delaware in and for New Castle County, Delaware, and of the United
          States Federal District Court sitting in the State of Delaware, such
          counsel is not aware of any legal or governmental proceeding, pending
          against the Trust;

          (g)  Butler & Binion, L.L.P., counsel for the Company and the Trust,
     shall have furnished to the Underwriters 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 Underwriters, 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 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 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 

                       

                                      -20-
<PAGE>
 
          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
          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)  the authorized capital stock of the Company conforms as to
          legal matters, in all material respects, to the description thereof
          contained in the Prospectus;

               (vi)  the shares of Nuevo Common Stock initially issuable upon
          the conversion of the Convertible Debentures and the Trust Preferred
          Securities have been duly authorized and reserved for issuance upon
          such conversion and, when issued upon such conversion, will be duly
          authorized, validly issued, fully paid and nonassessable and are not
          subject to any preemptive or similar rights;

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

               (viii)  the Guarantee has been duly authorized, executed and
          delivered by the Company and the Guarantee is a valid and binding
          agreement of the Company enforceable against the Company in accordance
          with its terms, subject to (x) bankruptcy, insolvency, moratorium,
          receivership, reorganization, liquidation, fraudulent conveyance or
          transfer and other similar laws relating to or affecting the rights
          and remedies of creditors generally, (y) principles of equity,
          including applicable law relating to fiduciary duties (regardless of
          whether considered and 

                                      -21-
<PAGE>
 
          applied in a proceeding in equity or at law), and (z) the effect of
          applicable public policy on the enforceability of provisions relating
          to indemnification or contribution;

               (ix)  the Indenture has been duly authorized, executed and
          delivered by the Company and is a valid and binding agreement of the
          Company enforceable against the Company in accordance with its terms,
          subject to (x) bankruptcy, insolvency, moratorium, receivership,
          reorganization, liquidation, fraudulent conveyance or transfer and
          other similar laws relating to or affecting the rights and remedies of
          creditors generally, (y) principles of equity, including applicable
          law relating to fiduciary duties (regardless of whether considered and
          applied in a proceeding in equity or at law), and (z) the effect of
          applicable public policy on the enforceability of provisions relating
          to indemnification or contribution;

               (x)  the Convertible Debentures have been duly authorized,
          executed and delivered by the Company in accordance with the
          provisions of the Indenture and, assuming they have been duly
          authenticated in accordance with the provisions of the Indenture,
          constitute valid and binding obligations of the Company enforceable in
          accordance with their terms, subject to (x) bankruptcy, insolvency,
          moratorium, receivership, reorganization, liquidation, fraudulent
          conveyance or transfer and other similar laws relating to or affecting
          the rights and remedies of creditors generally, (y) principles of
          equity, including applicable law relating to fiduciary duties
          (regardless of whether considered and applied in a proceeding in
          equity or at law), and (z) the effect of applicable public policy on
          the enforceability of provisions relating to indemnification or
          contribution;

               (xi)  the Registration Statement and the Prospectus and any
          amendments and supplements thereto (other than the financial
          statements and related schedules and other financial and statistical
          data therein, 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 and other financial and statistical data
          therein, as to which such counsel need express no belief) the
          Registration Statement and the prospectus included therein at the time
          the Registration Statement became effective contained 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 that the Prospectus, as amended or
          supplemented, if applicable, contained 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, not misleading;

               (xii)  the statements in the Prospectus under the captions "Risk
          Factors," "Nuevo's Financing I," "Description of the TECONS,"
          "Description of the 

                                      -22-
<PAGE>
 
          Guarantee," "Description of the Convertible Debentures," "Effect of
          Obligations under the Convertible Debentures and the Guarantee,"
          "Description of Debt Securities," "Description of the Capital Stock,"
          "Certain Anti-Takeover Provisions," "Description of Warrants,"
          "Description of Trust Preferred Securities," "Description of Trust
          Preferred Securities Guarantee," "Description of Existing
          Indebtedness" and "Plan of Distribution," in each case insofar as they
          describe legal documents or refer to statements of law or legal
          conclusions, are accurate in all material respects and present fairly
          the information required to be shown;

               (xiii)  the execution and delivery by the Company of this
          Agreement, the Declaration, the Guarantee and the Indenture and the
          performance by the Company of its obligations hereunder and
          thereunder, the issuance and sale of the Convertible Debentures by the
          Company and the consummation by the Company of the other transactions
          contemplated by this Agreement will not constitute a breach of or
          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 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 respective properties, and no consent,
          approval, authorization or order of, or qualification with, any
          governmental body or agency is required for the performance by the
          Company of its obligations under this Agreement, except such as may be
          required by the securities or blue sky laws of the various states in
          connection with the offer and sale of the Convertible Debentures, the
          Trust Preferred Securities and the Guarantee;

               (xiv)  to the best of such counsel's knowledge, other than this
          Agreement, the Declaration and the Trust Securities, there are no
          agreements or instruments binding on the Trust that are material to
          the Trust, and, to the best of such counsel's knowledge, there is no
          judgement, order or decree of any governmental body, agency or court
          having jurisdiction over the Trust;

               (xv)  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 

                                      -23-
<PAGE>
 
          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;

               (xvi)  although the discussion set forth in the Prospectus under
          the heading "Certain Federal Tax Consequences" does not purport to
          discuss all possible United States federal income tax consequences of
          the purchase, ownership and disposition of the Trust Preferred
          Securities, in such counsel's opinion such discussion constitutes, in
          all material respects, a fair and accurate summary of the United
          States federal income tax consequences of the purchase, ownership and
          disposition of the Trust Preferred Securities under current law; and

               (xvii)  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, Butler & Binion, L.L.P. may rely as to
     matters involving the application of laws other than the laws of the United
     States and the State of Delaware and New York, to the extent such counsel
     deems proper and to the extent specified 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.  Such counsel may
     rely as to matters of fact, to the extent such counsel deems proper, on
     certificates of responsible officers of the Trust and of the Company and
     certificates or other written statements of officials of jurisdictions
     having custody of documents respecting the corporate existence,
     qualification or good standing of the Trust and of the Company and its
     subsidiaries.  The opinion of such counsel 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.  With respect to the matters to be covered in
     subparagraphs (xi) and (xv) 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 

                                      -24-
<PAGE>
 
     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.

          (h)  Richards, Layton & Finger, special Delaware counsel for the
     Delaware Trustee shall have given to the Underwriters their written opinion
     dated the Closing Date or the Additional Closing Date, as the case may be,
     in form and substance satisfactory to the Underwriters, to the effect that:

               (i)  Wilmington Trust Company is a Delaware banking corporation,
          duly incorporated, validly existing and in good standing, with full
          power and authority to execute and deliver, and to carry out and
          perform its obligations under the terms of, the Declaration, the
          Indenture and the Guarantee;

               (ii)  Wilmington Trust Company has been authorized to perform its
          obligations under the Certificate of Trust, the Declaration, the
          Indenture and the Guarantee; the Declaration under Delaware law
          constitutes a legal, valid and binding obligation of Wilmington Trust
          Company, enforceable against it in accordance with its terms, subject
          to the effect upon the Declaration of (x) bankruptcy, insolvency,
          moratorium, receivership, reorganization, liquidation, fraudulent
          conveyance or transfer and other similar laws relating to or affecting
          the rights and remedies of creditors generally, (y) principles of
          equity, including applicable law relating to fiduciary duties
          (regardless of whether considered and applied in a proceeding in
          equity or at law), and (z) the effect of applicable public policy on
          the enforceability of provisions relating to indemnification or
          contribution;

               (iii)  no consent, approval of authorization of, or registration
          with or notice to, any Delaware banking authority is required for the
          execution, delivery or performance by Wilmington Trust Company of the
          Declaration, the Indenture or the Guarantee; and

               (iv)  Wilmington Trust Company has it principal place of business
          in the State of Delaware; Wilmington Trust Company satisfies for the
          Trust the requirements set forth in Section 3807(a) of the Business
          Trust Act.

          The opinion of Richards, Layton & Finger described above shall be
     rendered to the Underwriters at the request of the Company and shall so
     state therein.

          (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 the Additional Closing Date, as the case may
     be, KPMG Peat Marwick L.L.P. shall have furnished to the Underwriters
     letters, dated the respective dates of delivery 

                                      -25-
<PAGE>
 
     thereof, in form and substance reasonably satisfactory to the Underwriters,
     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 Underwriters shall have received on and as of the Closing
     Date or the Additional Closing Date, as the case may be, an opinion of
     Vinson & Elkins L.L.P., counsel to the Underwriters, with respect to the
     due authorization and valid issuance of the Trust Preferred Securities, the
     Registration Statement, the Prospectus and other related matters as the
     Underwriters 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 Trust Preferred Securities to be delivered on the Closing
     Date or the Additional Closing Date, as the case may be, shall have been
     approved for listing on the Exchange, subject to official notice of
     issuance;

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

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

     7.   Each of the Trust and the Company jointly and severally agree to
indemnify and hold harmless each Underwriter, each affiliate of any Underwriter
which assists such Underwriter in the distribution of the Trust Preferred
Securities 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
Trust or 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 

                                      -26-
<PAGE>
 
to make the statements therein not misleading, except insofar as such losses,
claims, damages or liabilities arise out of or are based on any untrue statement
or omission or alleged untrue statement or omission made in reliance upon and in
conformity with information furnished to the Trust or the Company in writing by
any Underwriter 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 and the Trust 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 Trust Preferred Securities 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 Underwriter agrees, severally and not jointly, to indemnify and hold
harmless the Trust, the Nuevo Trustees, the Company, its directors, its officers
who sign the Registration Statement and each person who controls the Trust or
the Company within the meaning of Section 15 of the Securities Act and Section
20 of the Exchange Act to the same extent as the foregoing indemnity from the
Trust and the Company to each Underwriter, but only with reference to
information relating to such Underwriter furnished to the Trust or the Company
in writing by such Underwriter expressly for use in the Registration Statement,
the Prospectus, any amendment 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 or which indemnity may be sought pursuant to either of the two
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
reasonable fees and expenses of such counsel related to such proceeding.  In any
such proceeding, 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 Trust, the Regular
Trustees, the Company, its directors, its officers who sign the Registration
Statement and such control persons of the Company shall be designated in 

                                      -27-
<PAGE>
 
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 and second paragraphs of
this Section 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
Trust and the Company on the one hand and the Underwriters on the other hand
from the offering of the Trust Preferred Securities or (ii) if the allocation
provided by clause (i) above is not permitted by applicable law or if the
Indemnified Person fails to give the notice referred to in the immediately
preceding paragraph, 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 Trust and the Company 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 Trust and the Company 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 Trust and the Company and the total underwriting
compensation 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 Trust Preferred Securities.  The relative fault of the Trust and
the Company 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 Trust or the Company by
the Underwriters and the parties' relative intent, knowledge, access to
information and opportunity to correct or prevent such statement or omission.

     The Trust, the Company and the Underwriters agree that it would not be just
and

                                      -28-
<PAGE>
 
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 reasonably 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 Trust Preferred Securities underwritten by it
and distributed to the public were offered to the public exceeds the amount of
any damages that such Underwriter has other wise 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
11(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 Trust Preferred Securities set forth opposite their
names in Schedule I hereto, and not joint.

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

     The indemnity and contribution agreements contained in Section 7 and the
representations and warranties of the Trust and the Company 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 Trust or the Company, its officers or directors or any other person
controlling the Trust or the Company and (iii) acceptance of and payment for any
of the Trust Preferred Securities.

     8.   Notwithstanding anything herein contained, this Agreement (or the
obligations of the several Underwriters with respect to the Option Trust
Preferred Securities) may be terminated in the absolute discretion of the
Underwriters, by notice given to the Company, if after the execution and
delivery of this Agreement and prior to the Closing Date (or, in the case of the
Option Trust Preferred Securities, 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
Underwriters, is material and adverse and which, in the judgment of the
Underwriters, makes it impracticable to market the Trust Preferred Securities
being delivered at 

                                      -29-
<PAGE>
 
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.

     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 Trust or the Company
to comply with the terms or to fulfill any of the conditions of this Agreement,
or if for any reason the Trust or the Company shall be unable to perform its
obligations under this Agreement or any condition of the Underwriters'
obligations cannot be fulfilled, the Company agrees to reimburse the
Underwriters or such Underwriters as have so terminated this Agreement with
respect to themselves, severally, for all out-of-pocket expenses (including the
reasonable fees and expenses of its counsel) reasonably 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
Trust, the Company, the Underwriters, each affiliate of any Underwriter which
assists such Underwriter in the distribution of the Trust Preferred Securities,
any controlling persons 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 Trust Preferred Securities 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
Underwriters jointly or by J.P. Morgan Securities Inc. on behalf of the
Underwriters, and any such action taken by J.P. Morgan Securities Inc. 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 by
certified or registered mail postage prepaid or by overnight delivery by a
nationally recognized delivery service or if transmitted by any standard form of
telecommunication.  Notices shall be deemed effective upon receipt.  Notices to
the Underwriters shall be given to the Underwriters, 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 or the Trust shall be
given to it at Nuevo Energy Company, 1331 Lamar, Suite 1650, Houston, Texas
77010; Attention: Michael D. Watford, or at such other address as the Company or
the Trust shall deliver to the Underwriters.

     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.

                                      -30-
<PAGE>
 
     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 FINANCING I

                              By:  NUEVO ENERGY COMPANY, as Sponsor


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


                              NUEVO ENERGY COMPANY


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

Accepted:  December 18, 1996

J.P. MORGAN SECURITIES INC.
SALOMON BROTHERS INC

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

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

                                      -31-
<PAGE>
 
                                  SCHEDULE I

<TABLE>
<CAPTION>
-----------                                                           ----------------------              
UNDERWRITER                                                                 NUMBER OF                     
                                                                        UNDERWRITTEN TRUST                
                                                                       PREFERRED SECURITIES               
                                                                          TO BE PURCHASED                 
<S>                                                                   <C> 
J.P. Morgan Securities Inc...........................................         1,000,000                   
Salomon Brothers Inc.................................................         1,000,000                   
                                                                              ---------                   
                                                                                                          
          Total......................................................         2,000,000                   
                                                                              =========                   
</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 

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<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.

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<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:____________________________
        Name:
        Title:


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