EXHIBIT 23.1

                      CONSENT OF INDEPENDENT ACCOUNTANTS

We hereby consent to the incorporation by reference in Registration Statement 
No. 333-72985 on Form S-3 of Annaly Mortgage Management, Inc. of our report 
dated February 5, 1999 appearing in this Annual Report on Form 10-K.

Deloitte & Touche LLP

New York, New York
March 31, 1999