UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 13G
                                (RULE 13d - 102)

             Information to be included in statements filed pursuant
           to Rules 13d-1(b), (c) and (d) and amendments thereto filed
                              pursuant to 13d-2(b)

                              (AMENDMENT NO.___ )*

                            Harken Energy Corporation
                                (Name of Issuer)

                          Common Stock, $0.01 par value
                         (Title of Class of Securities)

                                    412552309
                                 (CUSIP Number)


                                October 12, 2004
             (Date of Event which Requires Filing of this Statement)

 Check the appropriate box to designate the rule pursuant to which this
                               Schedule is filed:

                                [ ] Rule 13d-1(b)
                                [x] Rule 13d-1(c)
                                [ ] Rule 13d-1(d)


 *The remainder of this cover page shall be filled out for a reporting person's
  initial filing on this form with respect to the subject class of securities,
   and for any subsequent amendment containing information which would alter
                  disclosures provided in a prior cover page.

    The information required on the remainder of this cover page shall not be
 deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
           Act of 1934 ("Act") or otherwise subject to the liabilities
   of that section of the Act but shall be subject to all other provisions of
                        the Act (however, see the Notes).

                       (Continued on the Following Pages)

                                  (Page 1 of 6)




CUSIP No. 412552309                   13G                     Page 2 of 6 Pages


1.      NAMES OF REPORTING PERSONS
        I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

               The Tail Wind Fund Ltd.

2.      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

        (a) [ ] (b) [ ]

3.      SEC USE ONLY

4.      CITIZENSHIP OR PLACE OF ORGANIZATION

                A British Virgin Islands corporation

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH:

5.      SOLE VOTING POWER

                22,608,821

6.      SHARED VOTING POWER

                     0

7.      SOLE DISPOSITIVE POWER

                22,608,821

8.      SHARED DISPOSITIVE POWER

                     0

9.      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               22,608,821

10.     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9)
        EXCLUDES CERTAIN SHARES*       [ ]

11.     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

                     9.9%

12.     TYPE OF REPORTING PERSON*

                     CO

                      *SEE INSTRUCTIONS BEFORE FILLING OUT!




CUSIP No. 412552309                   13G                     Page 3 of 6 Pages


ITEM 1(a).      NAME OF ISSUER:

         Harken Energy Corporation (the "Issuer")

ITEM 1(b).      ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

       180 State Street, Suite 200
         Southlake, Texas  76092

ITEM 2(a).      NAME OF PERSON FILING:

       The name of the person filing this statement on Schedule 13G is The Tail
       Wind Fund Ltd. ("Tail Wind").  Tail Wind Advisory and Management Ltd. is
       the investment manager for Tail Wind and expressly disclaims equitable
       ownership of and pecuniary interest in any shares of Common Stock
       arising from its status as the investment manager.

ITEM 2(b).      ADDRESS OF PRINCIPAL BUSINESS OFFICE OR, IF NONE, RESIDENCE:

       The Bank of Nova Scotia Trust Company (Bahamas) Ltd.
       Windermere House
       404 East Bay Street
       P.O. Box SS-5539
       Nassau, Bahamas
       Attn:  Ngaire Strachan

ITEM 2(c).      CITIZENSHIP:

       The Tail Wind Fund Ltd. is a corporation duly formed under the laws of
       the British Virgin Islands.

ITEM 2(d).      TITLE OF CLASS OF SECURITIES:

       Common Stock

ITEM 2(e).      CUSIP NUMBER:

         412552309

ITEM 3.         IF THIS STATEMENT IS FILED PURSUANT TO RULE 13d-1(b), OR
                13d-2(b) OR (c), CHECK WHETHER THE PERSON FILING IS A:

     (a)        [ ] Broker or dealer registered under Section 15 of the
                    Exchange Act.

     (b)        [ ] Bank as defined in Section 3(a)(6) of the Exchange Act.

     (c)        [ ] Insurance company defined in Section 3(a)(19) of the
                    Exchange Act.

     (d)        [ ] Investment company registered under Section 8 of the
                    Investment Company Act.

     (e)        [ ] An investment adviser in accordance with Rule
                    13d-1(b)(1)(ii)(E).

     (f)        [ ] An employee benefit plan or endowment fund in accordance
                    with Rule 13d-1(b)(1)(ii)(F).

     (g)        [ ] A parent holding company or control person in accordance
                    with Rule 13d-1(b)(1)(ii)(G).

     (h)        [ ] A savings association as defined in Section 3(b) of the
                    Federal Deposit Insurance Act.

     (i)        [ ] A church plan that is excluded from the definition of an
                    investment company under Section 3(c)(14) of the Investment
                    Company Act;

     (j)        [ ] Group, in accordance with Rule 13d-1(b)(1)(ii)(J).

       If this statement is filed pursuant to Rule 13d-1(c), check this box [x]




CUSIP No. 412552309                   13G                     Page 4 of 6 Pages


ITEM 4.         OWNERSHIP.

     Provide  the  following  information  regarding  the  aggregate  number and
percentage of the class of securities of the issuer identified in Item 1.

        (a) Amount beneficially owned:

                           22,608,821 shares of Common Stock

                        Subject to the Ownership Limitation (defined below),
                 Tail Wind owns a total of 23,006,330 shares of Common Stock,
                 including (i) 1,788,889 shares of Common Stock held by Tail
                 Wind, (ii) 6,133,333 shares of Common Stock into which 36,800
                 shares of Series L Convertible Preferred Stock are
                 convertible, assuming a conversion price of $.60 and no
                 accrued dividends, which were issued to Tail Wind on May 28,
                 2004 ("Series L Preferred"), (iii) 7,666,667 shares of Common
                 Stock into which 46,000 shares of Series M Convertible
                 Preferred Stock are convertible, assuming a conversion price
                 of $.60 and no accrued dividends, which were issued to Tail
                 Wind on or about October 12, 2004 ("Series M Preferred"), (iv)
                 3,382,353 shares of Common Stock into which warrants are
                 exercisable which were issued to Tail Wind on May 28, 2004
                 ("Series L Warrants") and (v) 4,035,088 shares of Common Stock
                 into which warrants are exercisable which were issued to Tail
                 Wind on or about October 12, 2004 ("Series M Warrants").

                          In accordance with Rule 13d-4 under the Securities
                 Exchange Act of 1934, as amended, because the number of shares
                 of Common Stock into which the Reporting Person's Series L
                 Preferred, Series M Preferred, Series L Warrants and Series M
                 Warrants are convertible and exercisable are limited, pursuant
                 to the terms of such instruments, to that number of shares of
                 Common Stock which would result in the Reporting Person having
                 beneficial ownership of 9.9% of the total issued and
                 outstanding shares of Common Stock (the "Ownership
                 Limitation"), the Reporting Person disclaims beneficial
                 ownership of any and all shares of Common Stock that would
                 cause the Reporting Person's beneficial ownership to exceed
                 the Ownership Limitation.

                          Therefore, in accordance with the Ownership
                 Limitation, Tail Wind, based upon 207,551,995 shares of common
                 stock outstanding, beneficially owns 22,608,821 shares of
                 Common Stock and disclaims beneficial ownership of 397,509
                 shares of Common Stock.

        (b) Percent of class:

                          Tail Wind's aggregate beneficial ownership of
                 22,608,821 shares of Common Stock constitutes 9.9% of all of
                 the outstanding shares of Common Stock, based upon 205,763,106
                 shares of Common Stock outstanding as of August 2, 2004 plus
                 the 1,788,889 shares of Common Stock issued to Tail Wind on or
                 about October 8, 2004.

        (c) Number of shares as to which such person has:

                  (i) Sole power to vote or to direct the vote

                                 22,608,821

                 (ii) Shared power to vote or to direct the vote

                                 Not applicable.

                 (iii) Sole power to dispose or to direct the disposition of

                                 22,608,821

                 (iv) Shared power to dispose or to direct the disposition of

                                 Not applicable.


CUSIP No. 412552309                   13G                     Page 5 of 6 Pages


ITEM 5.         OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.

       If this statement is being filed to report the fact that as of the date
       hereof the Reporting Persons have ceased to be the beneficial owner of
       more than five percent of the class of securities, check the following
       [ ].


ITEM 6.         OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER PERSON.

       Not applicable.

ITEM 7.         IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH
                ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING
                COMPANY.

       Not applicable.

ITEM 8.         IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP.

       Not applicable.

ITEM 9.         NOTICE OF DISSOLUTION OF GROUP.

       Not applicable.


ITEM 10.        CERTIFICATION.

       By signing below the undersigned certifies that, to the best of its
       knowledge and belief, the securities referred to above were not acquired
       and are not held for the purpose of or with the effect of changing or
       influencing the control of the issuer of the securities and were not
       acquired and are not held in connection with or as a participant in any
       transaction having that purpose or effect.




CUSIP No. 412552309                   13G                     Page 6 of 6 Pages


                                    SIGNATURE

     After reasonable  inquiry and to the best of its knowledge and belief,  the
undersigned  certifies that the information set forth in this statement is true,
complete, and correct.


Dated: October 20, 2004                      THE TAIL WIND FUND LTD.



                                              By: /s/ Andrew P. MacKellar
                                              ---------------------------------
                                              Andrew P. MacKellar, Director