8-K

                       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.

EX-99

                                                                   Exhibit 99.1

Annaly's Merger with FIDAC Becomes Effective

    NEW YORK--(BUSINESS WIRE)--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. Annaly will continue to operate as a self-managed and
self-advised real estate investment trust, and FIDAC will operate as
Annaly's wholly-owned taxable REIT subsidiary.
    The Company is a Maryland corporation which owns and manages a
portfolio of investment securities. The Company's principal business
objective is to generate net income for distribution to stockholders
from the spread between the interest income on its investment
securities and the cost of borrowing to finance their acquisition.

    This news release and our public documents to which we refer
contain or incorporate by reference certain forward-looking statements
within the meaning of Section 27A of the Securities Act of 1933 and
Section 21E of the Securities Exchange Act of 1934. Forward-looking
statements which are based on various assumptions (some of which are
beyond our control) may be identified by reference to a future period
or periods or by the use of forward-looking terminology, such as
"may," "will," "believe," "expect," "anticipate," "continue," or
similar terms or variations on those terms or the negative of those
terms. Actual results could differ materially from those set forth in
forward-looking statements due to a variety of factors, including, but
not limited to, changes in interest rates, changes in yield curve,
changes in prepayment rates, the availability of mortgage-backed
securities for purchase, the availability of financing and, if
available, the terms of any financing, FIDAC's clients removal of
assets FIDAC manages, FIDAC's regulatory requirements, and competition
in the investment management business. For a discussion of the risks
and uncertainties which could cause actual results to differ from
those contained in the forward-looking statements, see "Risk factors"
in our Annual Report on Form 10-K for the fiscal year ended December
31, 2003. We do not undertake, and specifically disclaim any
obligation, to publicly release the result of any revisions which may
be made to any forward-looking statements to reflect the occurrence of
anticipated or unanticipated events or circumstances after the date of
such statements.

    CONTACT: Annaly Mortgage Management, Inc.
             Investor Relations
             1-888-8Annaly
             www.annaly.com