NUVEEN FLAGSHIP MULTISTATE TRUST I
497, 1998-06-30
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<PAGE>
 
                     Supplement Dated June 29, 1998 to the
                      Prospectus Dated September 12, 1997

                                ______________


                      NUVEEN FLAGSHIP MULTISTATE TRUST I
                  Nuveen Flagship Arizona Municipal Bond Fund
                 Nuveen Flagship Colorado Municipal Bond Fund
                  Nuveen Flagship Florida Municipal Bond Fund
           Nuveen Flagship Florida Intermediate Municipal Bond Fund
                      Nuveen Maryland Municipal Bond Fund
                Nuveen Flagship New Mexico Municipal Bond Fund
               Nuveen Flagship Pennsylvania Municipal Bond Fund
                 Nuveen Flagship Virginia 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 June 29, 1998, for Nuveen Flagship Florida Intermediate Municipal Bond
Fund of Nuveen Flagship Multistate Trust I, footnote 1 to the Class A Sales 
Charges and Commissions table on page 8 of the prospectus will be changed to 
read as follows:

(1) Nuveen pays Authorized Dealers a commission equal to the sum of 1% (0.75% 
and 0.50%, respectively, for Intermediate and Limited Term Funds) of the first 
$2.5 million, plus 0.50% of the next $2.5 million, plus 0.25% (0.50% for 
Intermediate Funds) of any amount over $5 million. Unless the Authorized Dealer 
waived the commission, you may be assessed a contingent deferred sales charge 
(CDSC) of 1% (0.75% and 0.50%, respectively, for Intermediate and Limited Term 
Funds) if you redeem any of your shares within 18 months of purchase. The CDSC 
is calculated on the lower of your purchase price or redemption proceeds.

Other references to the CDSC on redemptions of $1 million purchases of Class A 
Shares of the above-referenced funds elsewhere in the prospectus are similarly 
amended.
                                 ______________

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

Michael Davern will be the portfolio manager for the Arizona, Colorado and New
Mexico Funds. He is currently a Vice President of Nuveen Advisory, and formerly
a Vice President of Flagship Financial Inc.

Thomas O'Shaughnessy will be the portfolio manager of the Florida, Florida 
Intermediate and Pennsylvania Funds. He is currently a portfolio manager for 
Nuveen Advisory Corp.

Daniel Solender will be the portfolio manager of the Maryland and Virginia 
Funds. He is an Assistant Vice President of, and previously a portfolio manager 
for, Nuveen Advisory Corp.


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<PAGE>

                          SUPPLEMENT DATED JUNE 29, 1998
                   TO THE STATEMENT OF ADDITIONAL INFORMATION
                           DATED SEPTEMBER 12, 1997

                                 -------------

                      NUVEEN FLAGSHIP MULTISTATE TRUST I
                  Nuveen Flagship Arizona Municipal Bond Fund
                 Nuveen Flagship Colorado Municipal Bond Fund
                  Nuveen Flagship Florida Municipal Bond Fund
           Nuveen Flagship Florida Intermediate Municipal Bond Fund
                      Nuveen Maryland Municipal Bond Fund
                Nuveen Flagship New Mexico Municipal Bond Fund
               Nuveen Flagship Pennsylvania Municipal Bond Fund
                 Nuveen Flagship Virginia 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-51 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-49, 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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