NUVEEN INVESTMENT TRUST III
497, 1999-01-08
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                       SUPPLEMENT DATED JANUARY 11, 1999
                   TO THE PROSPECTUS DATED DECEMBER 3, 1998
 
                               ----------------
 
                          NUVEEN INVESTMENT TRUST III
                              Nuveen Income Fund
 
                               ----------------
 
  Nuveen is modifying the ways you can eliminate paying a sales charge when
purchasing Class A shares of the fund. 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 the 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 DECEMBER 3, 1998
 
                               ----------------
 
                          NUVEEN INVESTMENT TRUST III
                              Nuveen Income Fund
 
                               ----------------
 
  As of January 11, 1999, Nuveen is making the following changes relating to
the purchase of shares of the fund.
 
  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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