NUVEEN FLAGSHIP MULTISTATE TRUST III
497, 1999-01-08
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                   SUPPLEMENT DATED JANUARY 11, 1999 TO THE
                      PROSPECTUS DATED SEPTEMBER 30, 1998
 
                               ----------------
 
                     NUVEEN FLAGSHIP MULTISTATE TRUST III
                  Nuveen Flagship Georgia Municipal Bond Fund
                 Nuveen Flagship Louisiana Municipal Bond Fund
              Nuveen Flagship North Carolina Municipal Bond Fund
                 Nuveen Flagship Tennessee Municipal Bond Fund
 
                               ----------------
 
  Nuveen is modifying the ways you can eliminate paying a sales charge when
purchasing Class A shares of the funds. As of January 11, 1999, you will no
longer be able to purchase Class A shares at net asset value without a sales
charge using redemption proceeds from funds unaffiliated with Nuveen. The
other methods of eliminating the Class A sales charge described under "How to
Reduce Your Sales Charge" in each fund's prospectus will continue to be
available.
 
        PLEASE KEEP THIS WITH YOUR FUND PROSPECTUS FOR FUTURE REFERENCE
<PAGE>
 
                   SUPPLEMENT DATED JANUARY 11, 1999 TO THE
         STATEMENT OF ADDITIONAL INFORMATION DATED SEPTEMBER 30, 1998
 
                               ----------------
 
                     NUVEEN FLAGSHIP MULTISTATE TRUST III
                  Nuveen Flagship Georgia Municipal Bond Fund
                 Nuveen Flagship Louisiana Municipal Bond Fund
              Nuveen Flagship North Carolina Municipal Bond Fund
                 Nuveen Flagship Tennessee Municipal Bond Fund
 
                               ----------------
 
  As of January 11, 1999, Nuveen is making the following changes relating to
the purchase of shares of the funds.
 
    1. The initial minimum investment for a systematic investment plan has
  been lowered from $3,000 to $50 per share class per fund.
 
    2. For purposes of purchasing shares through a group purchase program,
  the initial minimum investment for each participant will be lowered from
  $3,000 to $50 per share class per fund, provided that the group initially
  invests at least $3,000 in the fund.
 
    3. The ability to purchase load-waived Class A shares using redemption
  proceeds from funds unaffiliated with Nuveen has been eliminated.
 
    4. Investors will be able to buy Class A shares at net asset value
  without a sales charge by using the proceeds of sales of Nuveen Exchange-
  Traded fund shares or the termination/maturity proceeds from Nuveen Defined
  Portfolios (formerly Nuveen Unit Trusts). You must provide Nuveen
  appropriate documentation that the fund sale or Defined Portfolio
  termination/maturity occurred not more than one year prior to reinvestment.
  In addition, investors also may buy Class A shares at net asset value
  without a sales charge by directing their monthly dividends from Nuveen
  Exchange-Traded funds.
 
                      PLEASE RETAIN FOR FUTURE REFERENCE


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