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                            SCHEDULE 14A INFORMATION

    Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act
                                    of 1934


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          Section 240.14a-12


                              Nuevo Energy Company
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                (Name of Registrant as Specified In Its Charter)



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   (Name of Person(s) filing Information Statement, if other than Registrant)

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                               [Nuevo Letterhead]

                       Supplement to Our Proxy Statement
                              dated April 14, 1999

                                  May 11, 1999


Dear Nuevo stockholder:

   
In connection with our 1999 annual meeting of stockholders, we have made several
changes to our 1999 Stock Incentive Plan. These changes are in response to
guidelines which institutional investors use to determine whether to vote shares
they own to approve a stock incentive plan. While these guidelines are either
consistent with our past practices in granting awards under our other stock
incentive plans or reflect the intent of our compensation committee in making
future awards, certain institutional investors prefer that these guidelines be
specifically incorporated in the plans, and that any variance from the
guidelines be submitted to stockholders for approval.
    

   
    

   
                           1999 STOCK INCENTIVE PLAN
    

We have made the following amendments to our 1999 Stock Incentive Plan:

   
GENERAL

The 1999 Stock Incentive Plan authorizes the issuance of up to one million
shares of stock to directors of Nuevo and executive officers, other key
employees and consultants of Nuevo and its subsidiaries. Although no change to
the group of persons who are eligible to participate in the plan has been
made; in order to clarify those individuals who may participate, the
eligibility requirements have been amended. The amendments provide for awards
to directors of Nuevo and executive officers, employees and individuals who act
as consultants of Nuevo or any of its subsidiaries who have the capability of
making a substantial contribution to our success.
    

EXERCISE PRICE OF OPTIONS MUST BE EQUAL TO OR GREATER THAN MARKET PRICE

Prior to the amendments, the 1999 Stock Incentive Plan provided that the
exercise price of stock options granted under the plan would be the market
price on the date of grant, unless our compensation committee approved a
different exercise price. This would allow our compensation committee to grant
options at less than the market price on the date of grant. In the past, all of
the stock options granted under our plans were granted at the market price on
the date of grant. We have amended the 1999 Stock Incentive Plan to formalize
this practice and specifically provide that we will not issue stock options
with an exercise price less than the market value on the date of grant.

OPTIONS ISSUED UNDER THE PLAN MAY NOT BE RE-PRICED

We have amended the 1999 Stock Incentive Plan to provide that we may not reduce
the exercise price of options granted under the plan or exchange outstanding
options for options with a lower exercise price. Our existing plans do not
prohibit the reduction of the exercise price of options or exchange of
outstanding options for new options with a lower exercise price. As described
in the proxy statement, during 1998, the compensation committee authorized the
reduction in the exercise price of options owned by persons who are not
executive officers or directors of the company. The exercise price of options
owned by executive officers and directors was not changed.

PROHIBITION ON DIVIDEND EQUIVALENTS FOR STOCK OPTIONS

Prior to the amendments, the 1999 Stock Incentive Plan allowed the compensation
committee to issue stock options which would entitle the holder to receive an
amount equal to any dividends which would have been paid on the common stock
issuable upon exercise of a stock option. The company has never granted options
with these dividend equivalents. The 1999 Stock Incentive Plan has been amended
to formalize past practice and specifically provide that such dividend
equivalents cannot be issued under the plan.


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AMENDMENT OF THE PLAN

Prior to its amendment, the 1999 Stock Incentive Plan allowed the compensation
committee to amend the plan without stockholder approval. Under certain
circumstances, the rules of the New York Stock Exchange would require
stockholder approval of amendments to the plan. However, we have amended the
1999 Stock Incentive Plan to provide that any of the following amendments
require stockholder approval to become effective:

     o    Any material increase in the number of shares subject to the plan;

     o    any amendment to the terms of outstanding Award Agreements which
          benefit the plan participant if such improvement relates to a
          material number of shares under the plan; and

     o    any extension of the class of persons entitled to receive awards
          under the 1999 Stock Incentive Plan covering a material number of
          shares subject to the plan.

   
Amendments affecting a number of shares in any of the foregoing categories
equal to or less than 10% of the shares subject to the plan will not be deemed
material unless such amendment provides for a decrease in the exercise price of
an option  (which may not be approved for any options). In addition, the 
compensation committee may approve changes to outstanding award agreements 
which benefit the holder of awards in connection with the termination of the 
employment of a holder of such awards.
    

We have also amended the plan to provide that we will not waive the enforcement
of any provision of an outstanding award grant, although this will not prohibit
the amendment of a grant as contemplated above.

MINIMUM VESTING PERIOD FOR PERFORMANCE SHARES

Prior to its amendment, the 1999 Stock Incentive Plan had no requirement for
minimum vesting for awards which involve the issuance of stock to employees
(generally referred to as "performance share" awards). We have amended the plan
to provide that any performance share awards or similar awards would have a
minimum one year vesting period. Generally, if employment terminates (or, in
the case of director grants, a director resigns) prior to vesting, the shares
would be forfeit. Vesting generally has exceptions for death and disability,
which exceptions usually permit early vesting.

In addition, we have amended the 1999 Stock Incentive Plan to provide that all
performance share awards will be made only if the compensation committee
determines that the award is made in place of cash or other compensation to
which the employee or director would have been entitled.

We do not expect performance shares to be a material component of executive
officer compensation. However, as described in the proxy statement, in order to
facilitate stock ownership by directors, we will permit our directors to elect
to acquire common stock at a 33% discount to market price rather than cash
director fees. Such common stock would be subject to a three year vesting,
which vesting period could be extended at the election of the director.

   
    

You may review a copy of the plan, as amended, at the Securities and Exchange
Commission's web site www.sec.gov, or may request a copy of the plan from us by
contacting Barbara Forbes, Director of Investor Relations, Nuevo Energy Company
1331 Lamar, Suite 1650, Houston, Texas 77010 or by calling (713) 756-1781.

   
    
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                                 EXHIBIT INDEX
 
Exhibit A                 1999 Stock Incentive Plan