NUVEEN FLAGSHIP MULTISTATE TRUST III
497, 1998-06-30
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<PAGE>
 
                     Supplement Dated June 29, 1998 to the
                      Prospectus Dated September 26, 1997
                                  __________

                     NUVEEN FLAGSHIP MULTISTATE TRUST III
                  Nuveen Flagship Alabama Municipal Bond Fund
                  Nuveen Flagship Georgia Municipal Bond Fund
                 Nuveen Flagship Louisiana Municipal Bond Fund
              Nuveen Flagship North Carolina Municipal Bond Fund
              Nuveen Flagship South Carolina Municipal Bond Fund
                 Nuveen Flagship Tennessee Municipal Bond Fund
                                   __________

This supplement provides new and additional information beyond that contained in
the Prospectus and should be read in conjunction with the Prospectus.

Effective July 1, 1998, the following changes in portfolio managers will take 
effect:

Thomas O'Shaughnessy will be the portfolio manager for the Alabama, Georgia, 
North Carolina, South Carolina and Tennessee Funds. He is currently a portfolio 
manager of Nuveen Advisory Corp. since 1991.

Michael Davern will be the portfolio manager for the Louisiana Fund. He is 
currently a Vice President of Nuveen Advisory Corp., and formerly a Vice 
President of Flagship Financial Inc.


                      PLEASE RETAIN FOR FUTURE REFERENCE
<PAGE>
 
                        SUPPLEMENT DATED JUNE 29, 1998
                  TO THE STATEMENT OF ADDITIONAL INFORMATION
                           DATED SEPTEMBER 26, 1997

                                ______________


                     NUVEEN FLAGSHIP MULTISTATE TRUST III
                  Nuveen Flagship Alabama Municipal Bond Fund
                  Nuveen Flagship Georgia Municipal Bond Fund
                 Nuveen Flagship Louisiana Municipal Bond Fund
              Nuveen Flagship North Carolina Municipal Bond Fund
              Nuveen Flagship South Carolina Municipal Bond Fund
                 Nuveen Flagship Tennessee Municipal Bond Fund

                                ______________

This supplement provides new and additional information beyond that contained in
the Statement of Additional Information and should be read in conjunction with
the Statement of Additional Information.

Effective June 29, 1998, the following are changes to the Statement of
Additional Information relating to the purchase of shares of the Funds:

     1.  The minimum purchase amount described on page S-43 for Class R shares
         of a Fund has been increased from $1 million to $2.5 million.

     2.  For purposes of rights of accumulation described on page S-41, an
         investor may also include the value on the purchase date of previously
         purchased shares of Nuveen exchange-traded funds to determine the
         appropriate volume discount for purchases of Class A Shares.

     3.  For purposes of purchasing Class A Shares of each of the Funds at net
         asset value without a sales charge, the eligibility requirements for
         employer-sponsored qualified defined contribution retirement plans are
         as follows: the number of employees required to allow a plan to
         participate is 25 employees, and the initial purchase amount of an
         eligible plan is $500,000. Municipal bond funds are not a suitable
         investment for individuals investing through retirement plans.


                      PLEASE RETAIN FOR FUTURE REFERENCE


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