DREYFUS PREMIER GNMA FUND, 497J, 1998-05-13

DREYFUS PREMIER GNMA FUND
497J, 1998-05-13

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                                        May 13, 1998



Securities and Exchange Commission
Judiciary Plaza
450 Fifth Street, N.W.
Washington, D.C. 20549


     Re:  Dreyfus Premier GNMA Fund
          Registration Statement File Nos. 33-9591; 811-4880
          CIK No: 804171

Dear Sir/Madam:

     Pursuant to Rule 497(j) under the Securities Act of 1933, please be
advised that there are no changes to the Prospectus and Statement of
Additional Information contained in Post-Effective Amendment No. 19 to the
Fund's Registration Statement on Form N-1A filed pursuant to Rule 485(b)
with the Securities and Exchange Commission on April 28, 1998.

     Please address any comments or questions to the attention of the
undersigned at (212) 922-6840.

                                        Very truly yours,



                                        Joni Lacks Charatan

Enclosure

cc:  Stroock & Stroock & Lavan LLP
     Ernst & Young LLP