Exhibit 23.1 INDEPENDENT AUDITORS' CONSENT We consent to the incorporation by reference in Registration Statement No. 333-74618 of Annaly Mortgage Management, Inc. on Form S-3 of our report dated March 15, 2002, appearing in this Annual Report on Form 10-K of Annaly Mortgage Management, Inc. for the year ended December 31, 2001. /s/ Deloitte & Touche New York, New York March 15, 2002