<PAGE>
 
                  Supplement Dated September 14, 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.

     As of September 11, 1998, the Nuveen Flagship Alabama Municipal Bond Fund 
was reorganized into the Nuveen Flagship All-American Municipal Bond Fund and is
no longer available.

     As of September 11, 1998, the Nuveen Flagship South Carolina Municipal
Bond Fund was reorganized into the Nuveen Flagship All-American Municipal Bond
Fund and is no longer available.


                      PLEASE RETAIN FOR FUTURE REFERENCE



© 2022 IncJournal is not affiliated with or endorsed by the U.S. Securities and Exchange Commission