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

                                  SCHEDULE 13G

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934
                              (AMENDMENT NO. ___)*



                                 DATA RACE, Inc.
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                                (Name of Issuer)



                          COMMON STOCK, NO PAR VALUE
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                         (Title of Class of Securities)



                                    237842109
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                                 (CUSIP Number)



*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 the
disclosures provided in a prior cover page.

The information required in 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 following page(s))

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                                Page 1 of 4 Pages





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     CUSIP No. 237842109              13G                Page 2 of 4 Pages
-----------------------------                    ------------------------------
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 1.    NAMES OF REPORTING PERSON
                S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

       Alpha Capital Aktiengesellschaft
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 2. CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:
                                                                 (a)   |_|
                                                                 (b)   |_|
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 3.    SEC USE ONLY
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 4.    CITIZENSHIP OR PLACE OF ORGANIZATION

       Liechtenstein
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                          5.   SOLE VOTING POWER
         NUMBER OF             3,262,257 shares of Common Stock
          SHARES       --------------------------------------------------------
       BENEFICIALLY       6.   SHARED VOTING POWER
         OWNED BY              None
           EACH        --------------------------------------------------------
         REPORTING        7.   SOLE DISPOSITIVE POWER
        PERSON WITH            3,262,257 shares of Common Stock
                       --------------------------------------------------------
                          8.   SHARED DISPOSITIVE POWER
                               None
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  9.     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING
         PERSON
                         3,262,257 shares of Common Stock
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  10.    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES
         CERTAIN SHARES                                                   |X|

         The aggregate amount in Row 9 represents the maximum amount of shares
         that Alpha Capital can beneficially control under a contractually
         stipulated 9.9% ownership restriction. The full conversion of Alpha
         Capital's debenture and exrcise of its warrants would exceed this
         restriction.
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  11.    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9
                      9.9%
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  12.    TYPE OF REPORTING PERSON
                      CO
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CUSIP NO. 237842109                                            PAGE 3 OF 4 PAGES
                                                                   ---  ---

ITEM 1 (a) NAME OF ISSUER: DATA RACE, Inc.

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

           6509 Windcrest Drive, Suite 120, Plano, TX 75024

ITEM 2 (a) NAME OF PERSON FILING: Alpha Capital Aktiengesellschaft

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

           Pradafant 7, Furstentums 9490, Vaduz, Liechtenstein

ITEM 2 (c) CITIZENSHIP: Liechtenstein

ITEM 2 (d) TITLE OF CLASS OF SECURITIES: Common Stock, No par value

ITEM 2 (e) CUSIP NUMBER:  237842109

ITEM 3 IF THIS STATEMENT IS FILED PURSUANT TO RULE 13D-1(B) OR
       13D-2(B):  Not applicable

ITEM 4 OWNERSHIP

         (a) AMOUNT BENEFICIALLY OWNED: 3,262,257 Shares of Common Stock

         (b) PERCENT OF CLASS: 9.9%

         (c) NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

             (i)   SOLE POWER TO VOTE OR DIRECT THE VOTE

                                3,262,257 Shares

             (ii)  SHARED POWER TO VOTE OR DIRECT THE VOTE

                                    0 Shares

             (iii) SOLE POWER TO DISPOSE OR TO DIRECT THE DISPOSITION OF

                                3,262,257 Shares

             (iv) SHARED POWER TO DISPOSE OR TO DIRECT THE DISPOSITION OF

                                    0 Shares



CUSIP NO. 237842109                                           PAGE 4 OF 4 PAGES
                                                                  ---  ---


ITEM 5 OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS

                                 Not applicable

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 A GROUP

                                 Not applicable

ITEM 9   NOTICE OF DISSOLUTION OF GROUP

                                 Not applicable



                                    SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

                                            July 12, 2001
                                ----------------------------------------
                                                 (Date)

                                           /s/ Konrad Ackermann
                                ----------------------------------------
                                               (Signature)

                                        Konrad Ackermann, Director
                                ----------------------------------------
                                              (Name/Title)