EXHIBIT 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in Registration Statements No. 333-105987 and No. 333-72985 of Annaly Mortgage Management, Inc. on Form S-3 of our report dated March 5, 2004, appearing in the Annual Report on Form 10-K of Annaly Mortgage Management, Inc. for the year ended December 31, 2003 and to the reference to us under the heading "Experts" in the Prospectus, which is part of these Registration Statements. /s/ Deloitte & Touche LLP New York, New York March 9, 2004