AMERICAN CENTURY GOVERNMENT INCOME TRUST
485BXT, 1999-07-02
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                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                    FORM N-1A

REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933             [X]


         File No. 2-99222

         Pre-Effective Amendment No. ____

         Post-Effective Amendment No._38_                           [X]

                                     and/or

REGISTRATION STATEMENT UNDER THE INVESTMENT COMPANY ACT OF 1940     [X]


         File No. 811-4363

         Amendment No._39_

                        (Check appropriate box or boxes.)


                    AMERICAN CENTURY GOVERNMENT INCOME TRUST
               __________________________________________________
               (Exact Name of Registrant as Specified in Charter)


                             American Century Tower
                     4500 Main Street, Kansas City, MO 64111
                    ________________________________________
                    (Address of Principal Executive Offices)


         Registrant's Telephone Number, including Area Code:  (816) 531-5575


         David C. Tucker, Esq., 4500 Main Street, Kansas City, MO 64111
       _________________________________________________________________
                     (Name and Address of Agent for Service)

          Approximate Date of Proposed Public Offering: August 1, 1999


It is proposed that this filing become effective:

     [ ] immediately upon filing pursuant to paragraph (b)
     [X] on August 1, 1999 pursuant to paragraph (b)
     [ ] 60 days after filing pursuant to paragraph (a)(1)
     [ ] on (date) pursuant to paragraph (a)(1)
     [ ] 75 days after filing pursuant to paragraph (a)(2)
     [ ] on (date) pursuant to paragraph (a)(2) of rule 485.

If appropriate, check the following box:

     [X] This post-effective amendment designates a new effective date for a
         previously filed post-effective amendment.
- --------------------------------------------------------------------------------
This  filing  is  being  made  to  extend  the  date  of  effectiveness  of  the
Registrant's   Post-Effective   Amendment   No.  37  to  August  1,  1999.   The
Post-Effective Amendment originally requested effectiveness as of July 6, 1999.

The following documents are hereby incorporated by reference:

*    Prospectuses  for each of the  funds  under  the  issuer  American  Century
     Government  Income Trust,  dated July 6, 1999 filed pursuant to Rule 485(a)
     on May 7, 1999 (Accession No. 0000776374-99-000004).

*    Statement of Additional  Information for American Century Government Income
     Trust,  dated July 6, 1999  filed  pursuant  to Rule  485(a) on May 7, 1999
     (Accession No. 0000776374-99-000004).

*    Part C to the Registration  Statement of American Century Government Income
     Trust,  dated July 6, 1999  filed  pursuant  to Rule  485(a) on May 7, 1999
     (Accession No. 0000776374-99-000004).

Registrant is extending  effectiveness of its Registration Statement in order to
incorporate comments provided to its manager by the staff of the Commission.
<PAGE>
                                   SIGNATURES

     Pursuant  to  the  requirements  of the  Securities  Act of  1933  and  the
Investment Company Act of 1940, the Registrant certifies that it has duly caused
this  Post-Effective  Amendment  No.  38 to be  signed  on  its  behalf  by  the
undersigned,  thereunto duly  authorized,  in the City of Kansas City,  State of
Missouri on the 2nd day of July, 1999.

                            AMERICAN CENTURY GOVERNMENT INCOME TRUST

                            By: /*/George A. Rio
                                George A. Rio
                                President and Principal Executive Officer


     Pursuant  to  the   requirements  of  the  Securities  Act  of  1933,  this
Post-Effective  Amendment No. 38 has been signed below by the following  persons
in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
                                                                      Date
<S>                                  <C>                           <C>
*George A. Rio                       President, Principal          July 2, 1999
- ---------------------------------    Executive and Principal
George A. Rio                        Financial Officer

*Maryanne Roepke                     Vice President, Treasurer     July 2, 1999
- ---------------------------------    and Principal Accounting
Maryanne Roepke                      Officer

*Albert A. Eisenstat                 Director                      July 2, 1999
- ---------------------------------
Albert A. Eisenstat

*Ronald J. Gilson                    Director                      July 2, 1999
- ---------------------------------
Ronald J. Gilson

*William M. Lyons                    Director                      July 2, 1999
- ---------------------------------
William M. Lyons

*Myron S. Scholes                    Director                      July 2, 1999
- ---------------------------------
Myron S. Scholes

*Kenneth E. Scott                    Director                      July 2, 1999
- ---------------------------------
Kenneth E. Scott

*Isaac Stein                         Director                      July 2, 1999
- ---------------------------------
Isaac Stein

*James E. Stowers III                Director                      July 2, 1999
- ---------------------------------
James E. Stowers III

*Jeanne D. Wohlers                   Director                      July 2, 1999
- ---------------------------------
Jeanne D. Wohlers
</TABLE>
/s/Charles C.S. Park
*by Charles C.S. Park,  Attorney in Fact
(pursuant to a Power of Attorney dated December 18, 1998).


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