ONE GROUP INVESTMENT TRUST
497J, 1998-05-01
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<PAGE>   1


                           RULE 497(j) CERTIFICATION


     Pursuant to the requirements of Rule 497(j) under the Securities Act of
1933, the Registrant certifies that the forms of prospectuses and Statement of
Additional Information that would have been filed under Rule 497(c) would not
have differed from those contained in Post-Effective Amendment No. 7 filed on
April 13, 1998 pursuant to Rule 485(b). The text of Post-Effective Amendment
No. 7 was filed electronically.


                                   The One Group Investment Trust
                                   Registrant




                                   /s/ JAMES F. LAIRD, JR.*
                                   -------------------------------
                                   James F. Laird, Jr.
                                   President



                                   *By: /s/ ALAN G. PRIEST
                                        --------------------------
                                        Alan G. Priest
                                        Attorney in Fact


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