SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT

                     PURSUANT TO SECTION 13 OR 15(d) OF THE
                       SECURITIES AND EXCHANGE ACT OF 1934


                Date of Report (Date of earliest event reported)
                                  June 4, 2004


                        Annaly Mortgage Management, Inc.
              ----------------------------------------------------
             (Exact Name of Registrant as Specified in its Charter)



         Maryland                1-13447                        22-3479661
    -----------------            -------                       ------------
State or Other Jurisdiction     (Commission                 (I.R.S. Employer
     Of Incorporation)         File Number)                 Identification No.)



      1211 Avenue of the Americas
              Suite 2902
          New York, New York                                       10036
          ------------------                                    -----------
    (Address of Principal Executive                             (Zip Code)
               Offices)


       Registrant's telephone number, including area code: (212) 696-0100


                                    No Change
        ----------------------------------------------------------------
          (Former Name or Former Address, if Changed Since Last Report)








 Item .  Other Events

     On June 4, 2004,  Annaly Mortgage  Management,  Inc. (NYSE:  NLY) announced
that the acquisition of Fixed Income  Discount  Advisory  Company  ("FIDAC") was
completed on June 4, 2004.  A copy of the press  release is furnished as Exhibit
99.1 to this report.






SIGNATURES


         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.


                                      ANNALY MORTGAGE MANAGEMENT, INC.



                                      By: /s/Kathryn Fagan
                                          --------------------------------
                                          Name:  Kathryn Fagan
                                          Title: Chief Financial Officer



Dated: June 4, 2004










                                  EXHIBIT INDEX
                                  -------------


Exhibit No.             Description
-----------             -----------

99.1                    Press Release, dated June 4, 2004 issued by Annaly
                        Mortgage Management, Inc.