EXHIBIT 32.1

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


                        CERTIFICATION OF CHIEF EXECUTIVE
                  OFFICER REGARDING PERIODIC REPORT CONTAINING
                              FINANCIAL STATEMENTS


        I, Michael A.J. Farrell, the Chairman of the Board of Directors, Chief
Executive Officer, and President of Annaly Mortgage Management, Inc. (the
"Company") in compliance with 18 U.S.C. Section 1350, as adopted pursuant to
Section 906 of the Sarbanes-Oxley Act of 2002, hereby certify that, the
Company's Quarterly Report on Form 10-Q for the period ended September 30, 2004
(the "Report") filed with the Securities and Exchange Commission:

        o  fully complies with the requirements of Section 13(a) or 15(d) of the
           Securities Exchange Act of 1934, as amended; and

        o  the information contained in the Report fairly presents, in all
           material respects, the financial condition and results of operations
           of the Company.




                                          /s/ Michael A.J. Farrell

                                          Michael A.J. Farrell

                                          Chairman of the Board of Directors,
                                          Chief Executive Officer, and President

                                          November 5, 2004