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                                                                   EXHIBIT 10.37
 
                              WARRANT CERTIFICATE

                     TO PURCHASE SHARES OF COMMON STOCK OF
                             INLAND RESOURCES INC.
             INCORPORATED UNDER THE LAWS OF THE STATE OF WASHINGTON
                 CERTIFICATE EVIDENCING THE NUMBER OF WARRANTS
                             SET FORTH IN SECTION 1


     1.   Basic Terms. This certifies that, for good and valuable consideration,
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John E. Dyer (the "Holder"), is entitled, subject to the terms and conditions of
this Warrant Certificate (the "Certificate"), to purchase 50,000 (post 1-for-10
reverse stock split) shares of the common stock, $.001 par value (the "Common
Stock"), of Inland Resources Inc. (the "Company"), subject to adjustment as
provided in this Certificate, from the Company at the Exercise Price (as defined
below), on delivery of this Certificate to the Company with the exercise form
duly executed and payment of the Exercise Price payable to the Company by
cashier's check or other immediately available funds, for all shares purchased.
One Warrant (herein so called) is required for the purchase of one share of
Common Stock, subject to adjustment as provided herein.

     2.   Expiration Date.  The right to exercise the Warrants evidenced by this
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Certificate shall expire at 12:00 a.m. PST on the tenth (10th) anniversary of
the effective date of this Certificate, provided, however, that if Holder's
employment by the Company as an executive officer is terminated for any reason
other than death or disability then the Warrants evidenced by this Certificate
shall expire ninety (90) days after such termination, but if termination is as a
result of death or disability then the Warrants may be exercised at any time
within one year after the termination of employment for such reason (the
"Expiration Date").

     3.   Exercise Price.  The purchase price per share of the Common Stock upon
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exercise of the Warrants (the "Exercise Price") shall be equal to $6.27 (post 1-
for-10 reverse stock split) per share, which is equal to or greater than the
fair market value per share on the date hereof.  The Exercise Price may be
adjusted from time to time pursuant to the terms of this Certificate.

     4.   Company's Warranties, Representations and Covenants.  The Company
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warrants, represents and covenants to the Holder that:

          (a) The Company has been duly incorporated and organized and is
     validly existing as a corporation in good standing under the laws of its
     state of organization.

          (b) The Warrants have been duly authorized and are the validly issued,
     fully paid and binding obligation of the Company.  The Common Stock of the
     Company issuable upon exercise of the Warrants are validly authorized and
     upon

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     payment of the Exercise Price shall be validly issued, fully paid and
     nonassessable Common Stock of the Company.

          (c) Common Stock deliverable on the exercise of the Warrants shall, at
     delivery, be fully paid and nonassessable, free from all taxes, liens, and
     charges with respect to the purchase.

          (d) The Company shall take any necessary steps to assure that the par
     value per share of the Common Stock is at all times equal to or less than
     the then current Exercise Price of the Common Stock issuable pursuant to
     this Certificate.

          (e) The Company shall at all times reserve and hold available
     sufficient shares of its Common Stock to satisfy the Common Stock issuable
     upon exercise of this Warrant.

          (f) The Company shall maintain its books and records in accordance
     with generally accepted accounting principles applied on a consistent
     basis.

          (g) The Company shall permit the Holder through his designated
     representatives to visit and inspect any of the properties of the Company,
     to examine its books and records, and to discuss its affairs, finances and
     accounts with and be advised as to the same by the officers of the Company
     at reasonable times and intervals, on the same basis as any other
     shareholder.

     The provisions of this Section shall continue for so long as the Holder
owns this Certificate.

     5.   Method of Exercise; Shares Issued Upon Exercise.  Exercise may be made
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of all or any part of the Warrants evidenced by this Certificate by surrendering
it, with the exercise form provided for herein duly executed by or on behalf of
the Holder, at the executive office of the Company, accompanied by payment in
full of the Exercise Price payable in respect of the Warrants being exercised.
The Warrants are exercisable at the option of the Holder in whole or in part at
any time prior to the Expiration Date.  If less than all of the Warrants
evidenced by this Certificate are exercised, the Company will, upon such
exercise, execute and deliver to the Holder a new certificate (dated the date
hereof) evidencing the Warrants not so exercised.  Unless the Common Stock
issuable upon exercise of the Warrants has been registered under the Securities
Act of 1933, as amended (the "1933 Act"), the certificates evidencing the Common
Stock issuable on exercise of the Warrants will bear the following legend:

     "The shares of stock of Inland Resources Inc. (the "Company") represented
     by this certificate have not been registered under the Securities Act of
     1933, as amended (the "1933 Act"), or under the securities laws of any
     state, and the Holder hereof cannot make any sale, assignment, or other
     transfer of any shares of such stock except pursuant to an offering of such
     shares duly registered under the 1933 Act and the

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     applicable state securities laws, or under such other circumstances that,
     in the opinion of counsel of the Holder hereof, does not require
     registration under the 1933 Act and any state securities laws.  Said shares
     are restricted securities within the meaning of Rule 144 promulgated under
     the 1933 Act and may be subject to the limitations upon resale set forth
     therein or in other rules and regulations under the 1933 Act;"

provided, however, that the Company agrees that whenever the shares of Common
Stock issuable upon exercise or conversion of this Warrant shall have been
beneficially held for three (3) years within the meaning of Rule 144(k) of the
1933 Act or any successor rule or statute or any shorter period of time allowed
by such successor rule or statute, and so long as the Holder is not an affiliate
of the Company within the meaning of Rule 144, if required by Rule 144 or such
successor rule or statute, then the Company shall remove all restrictive legends
and stop transfer restrictions at the written request of the owner of the shares
of Common Stock issuable on exercise or conversion of this Warrant.

     6.   Investment Representation of Holder.  Holder represents and warrants
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that the Warrants evidenced by this Certificate, and any Warrant Shares (herein
so called) purchased upon exercise of the Warrants, have been, or will be,
acquired or purchased as an investment for Holder's own account and not with a
view toward further distribution thereof.  It is expressly understood that the
Warrants cannot be transferred except pursuant to Section 9 hereof, and that the
Warrant Shares cannot be sold or transferred except pursuant to an effective
registration statement or an exemption from applicable securities laws.

     7.   Adjustment of Shares Purchasable.  The number of shares of Common
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Stock purchasable hereunder and the Exercise Price per share are subject to
adjustment from time to time as specified in this Certificate.

     8.   Exchange for Other Denominations.  This Certificate is exchangeable,
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on its surrender by the Holder to the Company, for new Certificates of like
tenor and date representing in the aggregate the number of Warrants and the
right to purchase the number of shares of Common Stock purchasable hereunder in
denominations designated by the Holder at the time of surrender.

     9.   Restrictions on Transfer.  During the lifetime of Holder, this
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Certificate shall be exercisable only by the Holder in person, by attorney or by
mail, on surrender of this Certificate, properly endorsed.  Neither this
Certificate nor the Warrants are transferable by Holder by operation of law or
otherwise, except that in the event of death or disability of Holder while
employed by the Company or a subsidiary, the Warrants may be exercised at any
time within one year after such death or disability by the duly appointed
personal representative of Holder, or by any person or persons who shall acquire
the Warrants directly from Holder by bequest or inheritance.

     10.  Adjustment of Shares.  Wherever this Certificate specifies a number of
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shares of Common Stock or an Exercise Price per share, the specified number of
shares of Common Stock to be received on exercise and the Exercise Price per
share shall be changed to reflect adjustments

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(which may require that additional securities or other property be delivered on
exercise) required by this section, as follows:

          (a) If a stock or property dividend is declared to the holders of
     shares of the same class of securities of the Company as is issuable upon
     exercise of Warrants, there shall be added with respect to each share of
     Common Stock issuable upon exercise of Warrants the amount of the dividend,
     stock or property, which would have been issued to the Holder had the
     Holder been the holder of record of such issuable share at the dividend
     record date.  Such additional stock or property resulting from such
     dividend shall be delivered without additional cost upon the exercise of
     Warrants.  Any distribution to the holders of Common Stock of the Company
     of any kind, other than a distribution of cash as a dividend out of profits
     of the Company for the current year of the dividend, shall be treated as a
     stock or property dividend for purposes of this Subsection 10(a).  If the
     Holder is entitled to  receive cash upon exercise of Warrants under this
     Subsection 10(a), the Holder may, at the Holder's option, elect to reduce
     the Exercise Price by all or part of the cash to be received by the Holder
     upon exercise under this Subsection 10(a).

          (b) If an increase has been effected in the number of outstanding
     shares of the same class of securities of the Company as is issuable upon
     exercise of Warrants by reason of a subdivision of such shares, the number
     of shares which may thereafter be purchased upon exercise of Warrants shall
     be increased with respect to each share issuable upon exercise of Warrants
     by the number of shares which could have been received by the Holder at the
     time of such subdivision had it been the holder of record of such issuable
     shares at the record and/or effective date of the subdivision.  In such
     event, the Exercise Price per share of Warrants shall be proportionately
     reduced.

          (c) If a decrease has been effected in the number of outstanding
     shares of the same class of securities of the Company as is issuable upon
     exercise of Warrants by reason of a reverse stock split, the number of
     shares which may thereafter be purchased upon exercise of Warrants shall be
     changed with respect to each share issuable upon exercise of Warrants to
     the number of shares which would have been held by the Holder at the time
     of said reverse stock split had the Holder been the holder of such issuable
     share at the record and/or effective date of the reverse stock split.  In
     such event, the Exercise Price per share shall be proportionately
     increased.

          (d) If there is a capital reorganization, reclassification of the
     capital stock of the Company, or any consolidation or merger of the Company
     with any other corporation or corporations, or if there is a sale or
     distribution of all or substantially all of the Company's property and
     assets, the Company shall make adequate provision so that there shall
     remain and be substituted under this Certificate with respect to each share
     issuable upon exercise of Warrants the stock, securities and/or assets
     which

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     would have been issuable or payable in respect of or in exchange for such
     issuable shares if the Holder had been the owner of such share on the
     applicable record date. All other provisions of this Certificate shall
     remain in full force and effect.

     11.  Notice of Adjustment.  On the happening of any event requiring an
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adjustment of the Exercise Price or the shares purchasable hereunder, the
Company shall immediately give written notice to the Holder stating the adjusted
Exercise Price and the adjusted number and kind of securities or other property
purchasable hereunder resulting from the event and setting forth in reasonable
detail the method of calculation and the facts upon which the calculation is
based.

     12.  Notice Requirement.  If at any time the Company proposes or is aware
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of any of the following transactions, the Company shall give written notice to
the Holder at least 30 days prior to the proposed transaction:  an anticipated
voluntary or involuntary dissolution, liquidation or winding up of the Company;
a merger or consolidation of the Company; the payment or declaration of a
dividend or distribution to shareholders of the Company; or the vote of
shareholders of the Company to amend the certificate or articles of
incorporation of the Company.  Such notice shall contain:  (a) the date on which
the proposed transaction is to take place; (b) the record date (which shall be
at least 30 days after the giving of the notice) of the proposed transaction;
(c) a brief description of the proposed transaction; (d) a brief description of
any dividends or other distributions to be made to holders of Common Stock as a
result of the proposed transaction; (e) a brief description of any other effect
of the proposed transaction on holders of Common Stock or this Certificate; and
(f) an estimate of the fair value of any dividends or other distributions to be
made to shareholders.

     13.  Fractional Shares.  The Company shall not be required upon the
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exercise of any of the Warrants evidenced hereby to issue any fractional shares,
but shall make an adjustment therefore in cash on the basis of the mean between
the low bid and high asked prices on the over-the-counter market as reported by
the NASD Automated Quotation System or the closing market price on a national
securities exchange on the trading day immediately prior to exercise, whichever
is applicable, or if neither is applicable, then on the basis of the market
value of any such fractional interest as shall be reasonably determined by the
Company.

     14.  Notice.  Any notice required or permitted by any party to this
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Certificate shall be in writing and may be delivered personally to the party
being given notice or to the person in charge of the office of the party being
given notice or by facsimile, national overnight courier service or by mail, at
the party's address indicated below, and any notice will be effective only upon
actual receipt by the party.  The addresses of the parties are as follows:

          Holder:             475 17th Street, Suite 1500
                              Denver, Colorado  80202

          Company:            475 17th Street, Suite 1500
                              Denver, Colorado 80202

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The names and addresses of persons to receive notice as stated in this Section
may be changed by notice given in accordance with this Section.

     15.  Parties.  This Certificate shall bind the respective successors and
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assigns of the parties.

     16.  Entire Agreement.  This Certificate represents the entire agreement of
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the parties with respect to the subject matter hereof and supersedes any prior
or contemporaneous oral or written agreements or understandings.  The terms of
this Certificate may be amended only by a written instrument executed by the
Company and the Holder.

     WITNESS the signature of the Company's authorized representative and the
acceptance of the terms hereof by the signature of the Holder dated effective
May 22, 1996.


                                    COMPANY:

                                    INLAND RESOURCES INC.



                                    By: /s/ Kyle R. Miller
                                       ----------------------------------------
                                            Kyle R. Miller, President

                                    HOLDER:


                                    /s/ John E. Dyer
                                    -------------------------------------------
                                    JOHN E. DYER

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                                 EXERCISE FORM


                   (To be executed by the Holder to purchase
                 Common Stock pursuant to the within Warrants)



_______________________________
_______________________________
_______________________________

     The undersigned hereby:  (1) irrevocably elects to purchase ______ shares
of the Company's Common Stock issuable upon the exercise of the within Warrants,
and encloses payment of $________________ therefor; (2) requests that a
certificate for the shares be issued in the name of the undersigned and
delivered to the undersigned at the address below; and (3) if such number of
shares is not all of the shares purchasable hereunder, that a new Certificate of
like tenor for the balance of the remaining Warrants be issued in the name of
the undersigned and delivered to the undersigned at the address below.


                                    
Date:
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                                    (Please sign exactly as name appears on
                                    Warrant Certificate)


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                                    Address
                                        
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