SCUDDER GNMA FUND
497J, 1999-06-23
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                                               Scudder, Kemper Investments, Inc.
                                               Two International Place
                                               Boston, MA  02110
                                               June 23, 1999

Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, DC  20549

RE:  Scudder   GNMA  Fund,   (Reg.   No.   2-82632)   (811-3699)   (the  "Fund")
     Post-Effective Amendment No. 19 to Registration Statement on Form N-1A.

Ladies and Gentlemen:

     Pursuant to Rule 497(j) under the Securities Act of 1933, as amended, the
Fund hereby certifies that the form of Statement of Additional Information that
would have been filed on behalf of the Fund pursuant to Rule 497(c) upon the
effectiveness of Post-Effective Amendment No. 19 to the Fund's Registration
Statement on Form N-1A (the "Amendment") does not differ from that contained in
the Amendment, which is the most recent amendment to such Registration Statement
and was filed electronically on June 21, 1999. The Fund further certifies that
the Prospectus does not differ from that which was filed as a part of the Fund's
Post-Effective Amendment No. 18 filed electronically on April 30, 1999.

     Comments or questions concerning this certificate may be directed to
Gregory Pottle at 617-295-3033.

                                                           Very truly yours,


                                                  By:      /s/ Caroline Pearson
                                                          ---------------------
                                                           Caroline Pearson
                                                           Assistant Secretary,
                                                           Scudder GNMA Fund





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