EXHIBIT 32.1

                        ANNALY MORTGAGE MANAGEMENT, INC.
                           1211 AVENUE OF THE AMERICAS
                                   SUITE 2902
                            NEW YORK, NEW YORK 10036


                                  CERTIFICATION

                         PURSUANT TO SECTION 906 OF THE

               SARBANES-OXLEY ACT OF 2002, 10 U.S.C. SECTION 1350

In connection with the annual report on Form 10-K of Annaly Mortgage Management,
Inc.. (the "Company") for the period ended December 31, 2004 to be filed with
Securities and Exchange Commission on or about the date hereof (the "Report"),
I, Michael A.J. Farrell, Chairman of the Board, President, and Chief Executive
Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley
Act of 2002, 18 U.S.C. Section 1350, that:


    3.   The Report fully complies with the requirements of Section 13(a) or
         15(d) of the Securities Exchange Act of 1934; and

    4.   The information contained in the Report fairly presents, in all
         material respects, the financial condition and results of operations of
         the Company at the dates of, and for the periods covered by, the
         Report.

It is not intended that this statement be deemed to be filed for purposes of the
Securities Exchange Act of 1934.

                                       /s/ Michael A.J. Farrell
                                       Michael A.J. Farrell
                                       Chairman of the Board of Directors, Chief
                                       Executive Officer, and President
                                       March 4, 2005