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                                                                   EXHIBIT 4(ii)

                          FORM OF SECOND AMENDMENT TO

                              JANUS INVESTMENT FUND

                          INVESTMENT ADVISORY AGREEMENT

                            JANUS EQUITY INCOME FUND

         THIS SECOND AMENDMENT is made this 31st day of July, 2001, between
JANUS INVESTMENT FUND, a Massachusetts business trust (the "Trust"), and JANUS
CAPITAL CORPORATION, a Colorado corporation ("JCC").

                                   WITNESSETH

         WHEREAS, the Trust and JCC are parties to an Investment Advisory
Agreement on behalf of Janus Equity Income Fund (the "Fund"), dated July 1,
1997, as amended January 31, 2000 (the "Agreement");

         WHEREAS, the parties desire to amend the Agreement as set forth in
greater detail below;

         WHEREAS, pursuant to Section 11 of the Agreement, any amendment to the
Agreement is subject to approval by (i) a majority of the Trustees, including a
majority of the Trustees who are not interested persons (as that phrase is
defined in Section 2(a)(19) of the Investment Company Act of 1940 (the "1940
Act")) of JCC and, if required by applicable law, (ii) by the affirmative vote
of a majority of the outstanding voting securities of the Fund (as that phrase
is defined in Section 2(a)(42) of the 1940 Act);

         WHEREAS, the parties have obtained Trustee approval as set forth above,
and the parties agree that a shareholder vote is not required to amend the
Agreement; and

         WHEREAS, the name of Janus Equity Income Fund has been changed to Janus
Core Equity Fund effective July 31, 2001;

         NOW, THEREFORE, in consideration of the premises and of the mutual
agreements set forth below, the parties agree to amend the Agreement as follows:

         1. All references to "Janus Equity Income Fund" shall be replaced with
"Janus Core Equity Fund."

         2. The parties acknowledge that the Agreement, as amended, remains in
full force and effect as of the date of this Amendment, and that this Amendment,
together with the Agreement and any prior amendments, contains the entire
understanding and the full and




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complete agreement of the parties and supercedes and replaces any prior
understandings and agreements among the parties respecting the subject matter
hereof.

         3. This Amendment may be contemporaneously executed in two or more
counterparts, each of which shall be deemed an original but all of which
together shall constitute one and the same instrument.

         IN WITNESS WHEREOF, the parties have caused their duly authorized
officers to execute this Amendment as of the date first above written.


                                          JANUS CAPITAL CORPORATION



                                          By:
                                             -----------------------------------
                                             Thomas A. Early, Vice President and
                                             General Counsel


                                          JANUS INVESTMENT FUND



                                          By:
                                             -----------------------------------
                                             Thomas H. Bailey, President