NUVEEN FLAGSHIP MULTISTATE TRUST III
                     ------------------------------------

           AMENDMENT AND RENEWAL OF INVESTMENT MANAGEMENT AGREEMENT
           --------------------------------------------------------


This Agreement made this 1st day of June, 2000 by and between Nuveen Flagship
Multistate Trust III, a Massachusetts business trust (the "Fund"), and Nuveen
Advisory Corp., a Delaware corporation (the "Adviser");

WHEREAS, the parties hereto are the contracting parties under that certain
Investment Management Agreement (the "Agreement") pursuant to which the Adviser
furnishes investment management and other services to the Trust; and

WHEREAS, the Agreement terminates August 1, 2000 unless continued in the manner
required by the Investment Company Act of 1940; and

WHEREAS, the Board of Trustees of the Trust, at a meeting called for the
purpose, have approved the amendment to the Agreement and the continuation of
the Agreement as amended until August 1, 2001 in the manner required by the
Investment Company Act of 1940.

NOW THEREFORE, the Trust and the Adviser hereby agree to amend the Agreement as
follows:

     For the services and facilities described in Section 1, an additional
     breakpoint is added to the existing management fee schedule. The last
     breakpoint in the existing Agreement of

              Rate                      Net Assets
              ----                      ----------
             .4750%              On assets of $2 billion and over

     shall be changed to:

              Rate                      Net Assets
              ----                      ----------
             .4750%              For the next $3 billion
             .4500%              On assets of $5 billion and over


NOW THEREFORE, in consideration of the mutual covenants contained herein and in
the Agreement as hereby amended, the Trust and the Adviser hereby agree to
continue the amended Agreement in effect until August 1, 2001 and ratify and
confirm the Agreement in all respects.

                                   NUVEEN FLAGSHIP MULTISTATE TRUST III


                                   By:      /s/ Gifford R. Zimmerman
                                       -----------------------------
                                            Vice President
ATTEST:


      /s/ Virginia L. O'Neal
----------------------------
      Assistant Secretary
                                   NUVEEN ADVISORY CORP.


                                   By:        /s/ Thomas C. Spalding
                                       -----------------------------
                                              Vice President
ATTEST:


      /s/ Larry W. Martin
-------------------------
      Assistant Secretary