CONVERSION/REDEMPTION AGREEMENT

EXHIBIT 10.3

CONVERSION/REDEMPTION AGREEMENT

This CONVERSION/REDEMPTION AGREEMENT (“Agreement”) is made as of this 7^th day of October, 2004 by and between HARKEN ENERGY CORPORATION, a Delaware corporation (the “Company”), THE TAIL WIND FUND LTD and SOLOMON STRATEGIC HOLDINGS, INC. (collectively with The Tail Wind Fund Ltd., “Holders”, and each a “Holder”).

WITNESSETH:

WHEREAS, pursuant to that certain Preferred Stock Purchase Agreement (“Purchase Agreement”) dated as of May 28, 2004 by and between the Company and the Holders, the Company sold and issued to the Holders on May 28, 2004, among other securities, an aggregate of 50,000 shares (“Preferred Shares”) of the Company’s Series L Cumulative Convertible Preferred Stock, liquidation preference $100 per share, having the rights, designations and preferences set forth in the Certificate of Designations for such Preferred Shares filed with the Secretary of State of the State of Delaware on May 28, 2004 (the “Designation”), which Preferred Shares are convertible into shares of the Company’s Common Stock (the “Underlying Shares”), in accordance with the terms of the Designation; capitalized terms used herein and not otherwise defined herein shall have the meanings ascribed thereto in the Purchase Agreement or Designation, as applicable;

WHEREAS, the Holders still own all of the originally issued Preferred Shares;

WHEREAS, the Underlying Shares are registered for resale pursuant to a registration statement originally filed with the SEC under the Securities Act of 1933, as amended (“Securities Act”), on July 22, 2004 and declared effective August 17, 2004 (“Registration Statement”); and

WHEREAS, in order to induce the Holders to convert their Preferred Shares as set forth herein, the Company wishes to reduce the Conversion Price under the Designation pursuant to Section 5(c)(vii) of the Designation for a limited time in consideration for the terms and conditions contained herein;

NOW THEREFORE, in consideration of the foregoing premises and the mutual covenants set forth in this Agreement, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1. Agreement to Convert. Subject to a redemption of such Preferred Shares pursuant to Section 2 below, each Holder hereby agrees to convert on the following dates (each an “Installment Date”) at least 20% of the Preferred Shares originally issued to such Holder: the date which is one (1) Trading Day following the date hereof, November 2, 2004, December 1, 2004, December 30, 2004 and February 1, 2005, provided that on such applicable Installment Date there exists Effective Registration. “Effective Registration” means (i) the resale of all Registrable Securities (as defined in the Registration Rights Agreement) is covered by an effective registration statement in accordance with the terms of the Registration Rights Agreement which registration statement is not subject to any suspension or stop orders; (ii) the resale of such Registrable Securities may be effected pursuant to a current and deliverable prospectus (including any applicable prospectus supplements) that is not subject at the time to

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any blackout or similar circumstance; (iii) such Registrable Securities are listed, or approved for listing prior to issuance, on the Nasdaq National or Small-Cap Market, the New York Stock Exchange or the American Stock Exchange, and are not subject to any trading suspension (nor shall trading generally have been suspended on such exchange or market), and the Company shall not have been notified of any pending or threatened proceeding or other action to delist or suspend the Common Stock on any of such markets on which the Common Stock is then traded or listed; (iv) the requisite number of shares of Common Stock has been duly authorized and reserved for issuance as required by the terms of the Purchase Agreement; and (v) the average of the VWAPs for the twenty (20) consecutive Trading Days immediately preceding the Conversion Date is greater than $0.25. For clarification, the terms and conditions relating to any conversion pursuant to this Section 1 are governed by the Designation (at the reduced Conversion Price as provided in Section 3 (below). Section 5(i) of the Designation shall not be deemed to restrict or in any way limit the Holder’s obligation to convert the Preferred Shares pursuant to this Section 1, provided that no Holder shall have the right to obtain shares of Common Stock under the Designation to the extent same would cause the Restricted Ownership Percentage to be exceeded.

2. Redemption by Company. In lieu of forcing any conversion pursuant to Section 1 above, the Company shall have the right to redeem for cash on each Installment Date 20% of the Preferred Shares originally issued to such Holder at a redemption price (“Installment Redemption Price”) equal to the Liquidation Value of such Preferred Shares on such Installment Date, provided that the Company shall deliver to the Holders written notice electing to so redeem in cash at least twenty (20) Trading Days prior to each such Installment Date on which the Company is electing to so redeem in cash. Each Holder shall be treated proportionately with respect to the Company’s election to redeem in cash. To the extent that any Holder elects not to convert any Preferred Shares pursuant to Section 1 above as of any Installment Date due to a lack of Effective Registration, then the Company shall redeem for cash on such Installment Date 20% of the Preferred Shares originally issued to such Holder at a redemption price equal to the Installment Redemption Price. In the event that the Company fails to timely issue Underlying Shares to any Holder following a conversion pursuant to Section 1 above, such Holder shall have the right to elect to have such Preferred Shares redeemed at the Installment Redemption Price instead. Any payment of the Installment Redemption Price pursuant to this Section 2 shall be paid on the applicable Installment Date, or if pursuant to the preceding sentence, within three (3) Trading Days following demand therefore. If the Installment Redemption Price is not paid within three (3) Trading Days of the due date, such amount shall bear interest at the lower of 18% or the highest rate permitted by law.

3. Conversion Price Reduction. Notwithstanding anything contained in the Designation, pursuant to Section 5(c)(vii) of the Designation, the Company hereby irrevocably reduces the Conversion Price as defined in the Designation for the period commencing on the day following the date hereof and ending on April 30, 2005 to a price equal to $0.52 for the first Installment Date and thereafter the average of the VWAPs for the twenty (20) consecutive Trading Days immediately preceding the applicable Conversion Date (“Pricing Period”). Each VWAP during the Pricing Period shall be appropriately and equitably adjusted in the event of any stock split, stock dividend, distribution or similar event consistent with Section 5(c) of the Designation. Contemporaneously with the execution of this Agreement the Company shall execute and deliver to the Holders by facsimile and mail, first class, postage prepaid a notice of such reduction in the form of notice attached hereto as Exhibit A.

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4. Registration Rights.

(a) Certain Representations. The Company represents that (i) up to 12,704,250 Underlying Shares issuable upon conversion of the Preferred Shares (whether pursuant to Section 2 above or otherwise), are registered for resale by the Holders, (ii) the Registration Statement is effective, and (iii) the resale of such Underlying Shares may be effected pursuant to the prospectus contained therein which is not subject to any blackout or similar circumstance. In addition, the Company shall file a current report on Form 8-K concerning the facts and material terms of this Agreement within (2) business days of the date hereof.

(b) New Registration Statement for Underlying Shares. If at any time the number of Underlying Shares issued and issuable upon full conversion of all Preferred Shares (without regard to any restrictions on beneficial ownership) exceeds 90% of the number of shares of Common Stock registered under the Registration Statement, then the Company shall (1) within five (5) Trading Days prepare a new registration statement on Form S-3 (or, if Form S-3 is not then available to the Company, on such form of registration statement as is then available to effect a registration for resale of such additional Registrable Securities) covering the resale of additional Underlying Shares in an amount equal to 130% of the number of Underlying Shares issued and issuable upon full conversion of the Preferred Shares at the Conversion Price as of the filing date (without regard to any restrictions on beneficial ownership), (2) use its best efforts to file such new registration statement with the SEC as soon as practicable, and (3) cause such new registration statement to be declared effective as soon as practicable following such filing. For clarification, the terms and conditions of the Registration Rights Agreement (including without limitation Section 2(c)(i) thereof) shall apply to such new registration statement, which shall constitute a “Registration Statement” thereunder, with the term “Closing Date” referring to the date on which such 90% threshold is exceeded.

(c) New Registration Statement for Warrants. The Company shall register for resale 130% of the Warrant Shares underlying the Warrants (without regard to any restrictions on beneficial ownership) in the registration statement that the Company will be filing pursuant to that certain registration rights agreement entered into on or about the date hereof between the Company and the Holders in connection with the Holders’ purchase of the Company’s Series M Cumulative Convertible Preferred Stock. The terms and conditions of such registration rights agreement (including without limitation Section 2(c)(i) thereof) shall apply to the registration of such Warrant Shares, and the Warrant Shares shall constitute “Registrable Securities” thereunder.

5. Miscellaneous.

(a) Full Force and Effect. Except as otherwise expressly provided herein, each of the Purchase Agreement, the Registration Rights Agreement, the Designation and the Warrants and the other agreements and transactions contemplated thereby shall remain in full force and effect.

(b) Warrants Clarification. In Section 3(a) of the Warrants the words “Exercise Date” mean the issuance date thereof, and such words shall therefore be replaced with “issuance hereof”.

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(c) Consent to Jurisdiction Etc. Each of the Company and each Holder agree that any legal action or proceeding relating to or arising out of or under this Agreement may be brought in the state or federal courts in the State of New York, County of New York, and each party accepts with regard to any such action or proceeding for itself and in respect to its property, generally and unconditionally, the jurisdiction of the aforesaid courts. Each party further irrevocably consents to the service of process out of any of the aforementioned courts in any such action or proceeding by the mailing of copies thereof by registered or certified U.S. mail, postage prepaid, to it at its addresses provided in the Purchase Agreement, such service to become effective upon receipt or five (5) days after such mailing, whichever shall first occur. To the fullest extent permitted by applicable law, each party hereby waives, and agrees not to assert, by way of motion, defense, counterclaim or otherwise, in any such suit, action or proceeding any claim that (i) it is not personally subject to the jurisdiction of any of the above-named courts by reason of any immunity or otherwise, (ii) its properties are exempt or immune from setoff, execution or attachment, either prior to judgment or in aid of execution or (iii) any suit, action or proceeding so brought is in an inconvenient forum or that the venue of the suit, action or proceeding is improper or that the subject matter hereof may not be enforced in or by such courts.

(d) Authority. Each party hereto hereby represents and warrants to the other party that the execution and delivery by such party of this Agreement, and the performance by such party of its obligations hereunder, have been duly and validly authorized by such party, with no other action on the part of such party being necessary. This Agreement has been duly and validly executed and delivered by such party and constitutes a legal, valid and binding obligation of such party enforceable against such party in accordance with its terms.

(e) Indemnification. Each party hereto hereby agrees to indemnify and hold harmless the other party against all losses, claims, damages, liabilities, costs (including without limitation reasonable attorney’s fees) and expenses imposed or incurred in connection with any breach or misrepresentation hereunder by such party or any enforcement of this indemnification.

(f) Governing Law. This Agreement shall be governed by and construed in accordance with the internal laws of the State of New York.

(g) Notices. All notices, requests and other communications hereunder must be in writing and will be deemed to have been duly given only if delivered personally, by courier or by facsimile transmission or mailed (first class postage prepaid) to the parties at the addresses or facsimile numbers set forth in the Purchase Agreement.

(h) Counterparts. This Agreement may be executed in any number of counterparts, each of which will be deemed an original, but all of which together will constitute one and the same instrument.

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(i) Further Assurances. Each party shall do and perform, or cause to be done and performed, all such further acts and things, and shall execute and deliver all such other agreements, certificates, instruments and documents, as the other party may reasonably request in order to carry out the intent and accomplish the purposes of this Agreement and the consummation of the transactions contemplated hereby.

***Signatures Appear on the Next Page***

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IN WITNESS WHEREOF, each of the parties hereto has caused this Agreement to be duly executed as of the date first written above.

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EXHIBIT A

Conversion Price Reduction Notice

HARKEN ENERGY CORPORATION

180 State Street, Suite 200

Southlake, TX 76092

VIA FACSIMILE AND FIRST CLASS MAIL

October 7, 2004

The Tail Wind Fund Ltd.

c/o Tail Wind Advisory and Management Ltd.

Attn: David Crook

1st Floor, No. 1 Regent Street

London, SW1Y 4NS UK

Facsimile: +011 (44) 207 ###-###-####

Solomon Strategic Holdings, Inc.

c/o Andrew P. MacKellar (Director)

Greenlands, The Red Gap

Castletown, IM9 1HB

British Isles

Facsimile: +011 (44) 1624 824191

Dear Sirs:

The Company hereby notifies The Tail Wind Fund Ltd. and Solomon Strategic Holdings, Inc., constituting all the holders of Preferred Shares, that, pursuant to Section 5(c)(vii) of the Certificate of Designation for the Preferred Shares filed with the Secretary of State of the State of Delaware on May 28, 2004 (“Designation”), the Company hereby irrevocably reduces the Conversion Price as defined in the Designation for the period commencing tomorrow and ending on April 30, 2005 to a price equal to $0.52 for the first Installment Date (as defined in the Agreement) and thereafter the average of the VWAPs for the twenty (20) consecutive Trading Days immediately preceding the applicable Conversion Date (“Pricing Period”). Each VWAP during the Pricing Period shall be appropriately and equitably adjusted in the event of any stock split, stock dividend, distribution or similar event consistent with Section 5(c) of the Designation. Capitalized terms used herein and not otherwise defined shall have the meanings ascribed thereto in the Designation.

Cc: Peter J. Weisman, Esq.