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                                                                    Exhibit 10.4

                            SUBSCRIPTION AGREEMENT

                          __________________________

     THE SHARES OF COMMON STOCK REFERRED TO HEREIN HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS.  THE
SHARES MAY NOT BE OFFERED FOR SALE, SOLD, PLEDGED, TRANSFERRED, OR OTHERWISE
DISPOSED OF UNTIL THE HOLDER THEREOF PROVIDES EVIDENCE SATISFACTORY TO THE
ISSUER (WHICH, IN THE DISCRETION OF THE ISSUER, MAY INCLUDE AN OPINION OF
COUNSEL SATISFACTORY TO THE ISSUER) THAT SUCH OFFER, SALE, PLEDGE, TRANSFER, OR
OTHER DISPOSITION WILL NOT VIOLATE APPLICABLE FEDERAL OR STATE SECURITIES LAWS.

     This Subscription Agreement (this "Agreement") is made and entered into by
and between Miller Exploration Company, a Delaware corporation (the
"Corporation"), and the undersigned (the "Purchaser") who is subscribing hereby
for 370,370 shares (the "Shares") of the Corporation's common stock, par value
$.01 per share (the "Common Stock").

     In consideration of the Corporation's agreement to sell the Preferred
Shares to the Purchaser, upon the terms and conditions set forth herein, the
Purchaser agrees and represents and warrants to the Corporation as follows:

A.  Subscription.
    ------------

     1.  The Purchaser hereby subscribes for the Shares and for the total dollar
amount (the "Purchase Price") set forth on the signature page below, which
Purchase Price shall be payable in cash by check or by wire transfer (or by such
other form of cash payment as the Corporation desires to accept).

     2.  The Purchaser understands, acknowledges, and agrees that:

         a.  In reliance upon applicable exemptions, the Shares have not been
     registered under the Securities Act of 1933, as amended (the "Securities
     Act"), and the rules and regulations thereunder or any state securities
     laws and the rules and regulations thereunder.

         b.  No federal or state agency has made any finding or determination
     as to the fairness of this Offering for investment or any recommendation or
     endorsement of the Shares.

         c.  Since the Shares have not been registered under the Securities Act
     or applicable state securities laws, the economic risk of the investment
     must be borne

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     indefinitely by the Purchaser, and the Shares cannot be sold,
     pledged, hypothecated, or otherwise transferred unless subsequently
     registered under the Securities Act and such laws, or an exemption from
     such registration is available, and there is compliance with the
     requirements of this Agreement; such registration under the Securities Act
     and such laws is unlikely at any time in the future; and the Corporation is
     not obligated to file a notification under Regulation A of the Securities
     Act or a registration statement under the Securities Act or any state
     securities laws.

         d.  No assignment, sale, pledge, hypothecation, transfer, exchange, or
     other disposition, or offer, of the Shares can be made without the prior
     written approval of the Corporation.  No transfer will be permitted by the
     Corporation, which, in the view of the Corporation, would jeopardize the
     Corporation's compliance with federal or state securities laws.

         e.  The Shares are speculative investments which involve a high degree
     of risk of loss by the Purchaser.

         f.  Due to the high degree of risk of loss, Shares only may be sold to
     persons who understand the nature of the Corporation and who are
     "Accredited Investors" (as defined in Rule 501(a) of Regulation D
     promulgated under the Securities Act).

B.   Representations, Warranties, and Agreements.
     -------------------------------------------

     1.  The Purchaser hereby represents, warrants, and agrees that:

         a.  The Purchaser is acquiring the Shares for his own account for
     investment, and not with a view to distribution, resale, subdivision, or
     fractionalization thereof; and the undersigned has no present plans to
     enter into any contract, undertaking, agreement, or arrangement for
     distribution, resale, subdivision, or fractionalization of any of the
     Shares.  In order to induce the Corporation to issue and sell the Shares
     subscribed for hereby to the undersigned, it is agreed that the Corporation
     will have no obligation to recognize the ownership, beneficial or
     otherwise, of the Shares comprising such Shares by anyone but the
     undersigned.

         b.  (i) The Purchaser can bear the economic risk of losing his entire
     investment; (ii) his overall commitment to investments which are not
     readily marketable is not disproportionate to his net worth, and his
     investment in the Shares will not cause such overall commitment to become
     excessive; (iii) he has adequate means of providing for his current needs
     and personal contingencies and has no need for liquidity in his investment
     in the Shares; and (iv) he has such knowledge and experience in financial
     and business matters that he is capable of evaluating the risks and merits
     of this investment.

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        c.  The Purchaser has carefully read or reviewed and is familiar with
     the Corporation's (i) Annual Report on Form 10-K for the year ended
     December 31, 1999 (the "10-K") and (ii) Quarterly Report on Form 10-Q for
     the three months ended March 31, 2000.  The Corporation has made available
     to the Purchaser and/or his attorney and/or his accountant all agreements,
     documents, records, and books that he or they have requested relating to an
     investment in the Corporation.  The Purchaser and/or his attorney and/or
     his accountant all have had an opportunity to ask questions of and receive
     answers from the Corporation, or a person or persons acting on its behalf,
     concerning the terms and conditions of this investment, and answers have
     been provided to all of his or their questions concerning an investment in
     the Corporation.  In evaluating the suitability of an investment in the
     Corporation, the Purchaser has not been furnished and has not relied upon
     any representations or other information (whether oral or written) other
     than as contained in any documents, information, or answers to questions so
     furnished to him by the Corporation.

         d.  The Purchaser recognizes that investment in the Corporation
     involves certain risks, and he has taken full cognizance of and understands
     all of the risk factors related to the purchase of the Shares, including,
     but not limited to, those set forth under the caption "Risk Factors" in the
     10-K.

         e.  The Purchaser has discussed with his professional legal, tax, and
     financial advisors the suitability of the investment in the Corporation for
     his particular tax and financial situation.  All information which the
     Purchaser has provided to the Corporation concerning himself and his
     financial position is correct and complete as of the date set forth below,
     and, if there should be any material change in such information prior to
     the acceptance of the Purchaser's subscription and the sale of the Shares,
     he will immediately provide such information to the Corporation.

         f.  If this Agreement is executed and delivered on behalf of a
     partnership, corporation, trust, pension plan, estate, or other entity, (i)
     the person signing this Agreement on behalf of such entity has been duly
     authorized to execute and deliver this Agreement and all other instruments
     executed and delivered on behalf of such partnership, corporation, trust,
     pension plan, estate, or other entity in connection with the purchase of
     the Shares; (ii) the signature of the person signing this Agreement is
     binding upon such partnership, corporation, trust, pension plan, estate, or
     other entity; and (iii) the Purchaser was not organized for the specific
     purpose of acquiring the Shares.

         g.  The address set forth below is the Purchaser's true and correct
     residence or principal place of business, and the Purchaser has no present
     intention of becoming a resident of any other state or jurisdiction or
     moving its principal place of business.

         h.  The undersigned Purchaser is an "Accredited Investor" (as defined
     in Rule 501(a) of Regulation D promulgated under the Securities Act).

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         i.  The undersigned understands and agrees, and acknowledges that it
     has been disclosed to him, that the following restrictions and limitations
     are applicable to the undersigned's purchase and resales, pledges,
     hypothecations, or other transfers of the Shares, and, therefore, that the
     undersigned must bear the economic risk of investment in the Shares for an
     indefinite period of time as described in subparagraph A. 4. h.:

          (i)    The Shares have not been registered, as described in
          subparagraph A. 4. f. above and, therefore, cannot be sold, pledged,
          hypothecated, or otherwise transferred unless they are registered
          under the Securities Act and applicable state securities laws, or an
          exemption from such registration is available.

          (ii)   A legend has been placed on the certificates representing the
          Shares in substantially the following form:

                 THE SHARES OF STOCK REPRESENTED BY THIS CERTIFICATE HAVE NOT
                 BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED,
                 OR ANY STATE SECURITIES LAWS. THE SHARES MAY NOT BE OFFERED FOR
                 SALE, SOLD, PLEDGED, TRANSFERRED, OR OTHERWISE DISPOSED OF
                 UNTIL THE HOLDER HEREOF PROVIDES EVIDENCE SATISFACTORY TO THE
                 ISSUER (WHICH, IN THE DISCRETION OF THE ISSUER, MAY INCLUDE AN
                 OPINION OF COUNSEL SATISFACTORY TO THE ISSUER) THAT SUCH OFFER,
                 SALE, PLEDGE, TRANSFER, OR OTHER DISPOSITION WILL NOT VIOLATE
                 APPLICABLE FEDERAL OR STATE SECURITIES LAWS.

          (iii)  Stop transfer instructions have been or will be placed with
          respect to the Shares so as to restrict the resale, pledge,
          hypothecation, or other transfer thereof.

          (iv)   The legend and stop transfer instructions described in
          subparagraphs (ii) and (iii) above will be placed with respect to any
          new certificate issued upon presentment by the undersigned of a
          certificate for transfer for so long as such legend and instructions
          are deemed advisable by the Corporation.

          j.    It has never been represented, guaranteed or warranted to the
     undersigned by the Corporation, its agents or employees, or any other
     person, expressly or by implication, any of the following:

          (i)   The appropriate or exact length of time that the undersigned
          will be required to remain as owner of the undersigned's Shares.

                    OR
                    --

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          (ii)   The percentage of profit and/or amount or type of
          consideration, profit, or loss (including tax writeoffs and/or tax
          benefits) to be realized, if any, as a result of this investment.

          k.     If the undersigned Purchaser is an individual, initial below:

-----                 (i)   The net worth (i. e., total assets minus total
Initial if         liabilities) at the date hereof of the undersigned, or joint
Applicable         net worth with the undersigned's spouse, exceeds $ 1,000,000.

                                OR
                                --

-----                 (ii)  The undersigned had individual income (not including
Initial if          spouse's income) in excess of $200,000 in each of the two
Applicable          most recent years or joint income with spouse in excess of
                    $300,000 in each of those years and reasonably expects to
                    reach the same income level in the current year.

     The undersigned's United States social security number is ---_____________.

          l.  If the undersigned Purchaser is an entity, initial below:

-----                 (i)  Each of the equity owners of the undersigned is an
Initial if          individual and satisfies at least one of the tests set forth
Applicable          in subparagraphs (k)(i) or (k)(ii) above.  (If this item has
                    been initialed, have each of such equity owners execute and
                    furnish a Certificate of Financial Position in the form of
                    Schedule 1 hereto).

                    OR
                    --

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-----                (ii)  The entity is an organization described in section
Initial if         501(C)(3) of the Internal Revenue Code of 1986, as amended,
Applicable         corporation, a Massachusetts or similar business trust, or a
                   partnership, not formed for the specific purpose of acquiring
                   the Shares, with total assets in excess of $5,000,000.


     The undersigned's United States employer identification number is
____________________.  The undersigned's place of incorporation or organization
is ___________________.

     2.  The foregoing representations and warranties are true and accurate as
of the date hereof and shall be true and accurate as of the date of the
acceptance hereof by the Corporation and the sale of the Shares to the
Purchaser.  If in any respect such representations and warranties shall not be
true and accurate prior thereto, the Purchaser will give written notice of such
fact to the Corporation specifying which representations and warranties are not
true and accurate and the reasons therefor.

C.   Miscellaneous.
     -------------

     1.  All pronouns and any variations thereof used herein shall be deemed to
refer to the masculine, feminine, neuter, singular, or plural as the identity of
the person or persons may require.

     2.  Notices required or permitted to be given hereunder shall be in writing
and shall be deemed to be sufficiently given when personally delivered or when
sent by registered or certified mail, return receipt requested, (i) if to the
Purchaser, at the address set forth on the signature page hereof, and (ii) if to
the Corporation, at 3104 Logan Valley Road, Traverse City, Michigan 49685, as
either of such addresses may be changed from time to time by notice given in
accordance with this paragraph.

     3.  Failure of the Corporation to exercise any right or remedy under this
Agreement or any other agreement between the Corporation and the Purchaser, or
otherwise, or delay by the Corporation in exercising same, will not operate as a
waiver thereof.  No waiver by the Corporation will be effective unless and until
it is in writing and signed by the Corporation.

     4.  This Agreement shall be enforced, governed, and construed in all
respects in accordance with the laws of the State of Delaware.  This Agreement
and the rights, powers, and duties set forth herein shall be binding upon the
Purchaser, his heirs, estate, legal representatives, successors, and assigns and
shall inure to the benefit of the Corporation, its successors, and assigns.  In
the event that any

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provision of this Agreement is invalid or unenforceable under
any applicable statute or rule of law, then such provision shall be deemed
inoperative to the extent that it may conflict therewith and shall be deemed
modified to conform with such statute or rule of law.  Any provision hereof
which may prove invalid or unenforceable under any law shall not affect the
validity or enforceability of any other provision hereof.

     5.  This Agreement constitutes the entire agreement between the parties
hereto with respect to the subject matter hereof and may be amended only by a
writing executed by all parties.

                                       7
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                               _________________
                            Subscription Agreement
                                SIGNATURE PAGE


     IN WITNESS WHEREOF, the Purchaser has executed this Agreement as of the
11th day of July, 2000.

  Number of Preferred Shares               Ecco Investments, L.L.C.
  subscribed for at                        ------------------------------------
  $1.35 per Share:                         Print name(s) of Purchaser(s)

                                           ------------------------------------
  370,370

  Total Purchase Price:                    By:
                                                -------------------------------
                                                        Signature(s) of

  $499,999.50                              ------------------------------------
                                           ------------------------------------
                                           Robert M. Boeve, Member
                                           ------------------------------------
                                           Print title of person signing, if
                                           signing as an authorized
                                           representative of Purchaser

Make check payable to the order of:        Address of Purchaser's residence or
Miller Exploration Company                 principal place of business (Please
                                           print or type):

                                           ------------------------------------
                                           ------------------------------------
                                           ------------------------------------


   ___  Individual Ownership                              ___  Trust
   ___  Separate Property                                 ___  Corporation
   ___  Community Property                                ___  Pension Plan
   ___  Joint Tenancy(1)                                  ___  Estate
   ___  Tenancy in Common(1)(2)                            X   Other (please
                                                          ___
                                                          indicate  L.L.C.
                                                                    ______
----------------------

(1) Each person involved is be required to be an "Accredited Investor."
(2)  Both husband and wife must sign.
------------------------------------------------------

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Subscription for 370,370 Shares at $1.35 per Share, for a total of $499,999.50,
accepted as of July 11, 2000.

                         MILLER EXPLORATION COMPANY


                         By:  _______________________
                         Name:_______________________
                         Title:______________________

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                               INDIVIDUAL, JOINT
                           OR PARTNER ACKNOWLEDGMENT

STATE OF _______________________

COUNTY OF ______________________

  The undersigned Notary Public does hereby certify that on this _____ day of
_______________, 2000, personally appeared _________________________* known to
me to be the person whose name is subscribed to the foregoing instrument, who,
being by me duly sworn, declared and acknowledged to me that the same was his
free act and deed and that he executed and delivered same for the purposes and
consideration therein expressed and in the capacity therein stated, and that the
statements therein contained are true.


                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------
*  Insert name of individual or joint tenant or partner executing on behalf of
partnership.


            ACKNOWLEDGMENT BY HUSBAND AND WIFE AS TENANTS IN COMMON

STATE OF _______________________

COUNTY OF ______________________

  The undersigned Notary Public does hereby certify that on this _____ day of
________________, 2000, personally appeared __________________________ and
_________________________* known to me to be the persons whose names are
subscribed to the foregoing instrument, who, being by me duly sworn, declared
and acknowledged to me that the same were their free acts and deeds and that
they executed and delivered such instrument for the purposes and consideration
therein expressed and in the capacity therein stated, and that the statements
contained therein are true.

                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------
*  Insert names of husband and wife.

                                       10
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                   LIMITED LIABILITY COMPANY ACKNOWLEDGMENT

STATE OF _______________________

COUNTY OF ______________________

  On this 11th day of July, 2000, before me appeared Robert M. Boeve to me
personally known, who, being by me duly sworn, declared and acknowledged to me
that he is a member of Ecco Investments, L.L.C. and that the foregoing
instrument was executed and delivered on behalf of said limited liability
company by authority of the members and said Robert M. Boeve acknowledged said
instrument to be the free act and deed of said limited liability company, and
that the statements therein contained are true.

                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------

                 TRUST, PENSION PLAN, OR ESTATE ACKNOWLEDGMENT

STATE OF _______________________

COUNTY OF ______________________

  On this _____ day of ________________, 2000, before me appeared
__________________________* to me personally known, who, being by me duly sworn,
declared and acknowledged to me that he is the Trustee, Administrator, or
Executor of the _________________________** and that the foregoing instrument
was executed and delivered on behalf of said Trust, Pension Plan, or Estate by
authority of its Trustee, Administrator, or Executor and said
__________________________* acknowledged said instrument to be the free act and
deed of said Trust, Pension Plan, or Estate, and that the statements therein
contained are true.


                         -----------------------------
                         Notary Public
                         My Commission Expires:
                                                -------
----------
*  Insert name of Trustee, Administrator, or Executor.
**  Insert name of Trust, Pension Plan, or Estate.

                                       11
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                                  SCHEDULE 1

                       CERTIFICATE OF FINANCIAL POSITION



  This Certificate of Financial Position is provided by the undersigned pursuant
to subparagraph B.1.1.(i) of the Subscription Agreement (the "Subscription
Agreement") executed by the Purchaser named below relating to a subscription for
Miller Exploration Company, a Delaware corporation (the "Corporation").

  The undersigned represents and warrants to the Corporation that:

-----            (i)  The net worth (i.e., total assets minus total liabilities)
Initial if     at the date hereof of the undersigned, or joint net worth with
Applicable     the undersigned's spouse, exceeds $1,000,000.  The undersigned
               undertakes to inform the Corporation immediately if such net
               worth is less than $1,000,000 prior to the acceptance by the
               Corporation of the Purchaser's subscription.

               OR
               --

-----            (ii)  The undersigned had individual income (not including
Initial if     spouse's income) in excess of $200,000 in each of the two most
Applicable     recent years or joint income with spouse in excess of $300,000
               in each of those years and reasonably expects to reach the same
               income level in the current year.  The undersigned undertakes
               to inform the Corporation immediately if this representation
               and warranty becomes untrue prior to the acceptance by the
               Corporation of the Purchaser's subscription.



Dated:
-----
               -------------------------------
               (Signature)

               Name:
                      ------------------------
                      (Please Print)


               -------------------------------
               Relationship to Purchaser


               -------------------------------
               Name of Purchaser

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