AMERICAN CENTURY GOVERNMENT INCOME TRUST
497J, 1998-03-06
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                          American Century Investments
                                4500 Main Street
                          Kansas City, Missouri 64111

March 6, 1998


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

RE:  American Century Government Income Trust
          1933 Act File No. 2-99222
          1940 Act File No. 811-4363

Ladies and Gentlemen: 

     Pursuant to Rule 497(j) under the Securities  Act of 1933, as amended,  the
undersigned  hereby  certifies  that the form of  prospectus  and  statement  of
additional  information that would have been filed under paragraph (b) or (c) of
Rule 497 with respect to the  above-referenced  issuer  would not have  differed
from that contained in Post-Effective Amendment No. 35, filed February 27, 1998,
to the issuer's Registration Statement on Form N-1A.

     Any concerns regarding this filing should be directed to the undersigned at
(650) 967-9683.


Sincerely,

/s/Charles C.S. Park
Charles C.S. Park
Assistant General Counsel


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