UNITED MUNICIPAL HIGH INCOME FUND INC
497, 1997-05-30
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SUPPLEMENT TO THE PROSPECTUS

United Municipal High Income Fund, Inc. Class A Shares

The following information supplements and supersedes any contrary information
contained in the Prospectus:

At a special meeting of shareholders scheduled for July 24, 1997, shareholders
of the Fund will be asked to approve proposals relating to the following:

1.  Investment Restrictions.  Shareholders of the Fund will be asked to approve
elimination of or changes to certain of the Fund's fundamental investment
restrictions.  If approved, the current fundamental restrictions regarding
mortgaging or pledging securities, arbitrage transactions, securities owned by
affiliated persons and options, futures contracts, forward currency contracts
and other derivative instruments would be eliminated.  Also, if approved, the
current fundamental restrictions regarding diversification, investments in
commodities and commodity contracts, loans, margin purchases and short sales
would be modified.

If the foregoing changes to the Fund's fundamental investment restrictions are
approved, the Fund intends to implement new non-fundamental, operating policies
regarding derivative instruments and mortgaging or pledging securities.  These
operating policies would be in addition to the other non-fundamental
restrictions and policies set forth in the prospectus and Statement of
Additional Information and could be changed by the Board of Directors without
shareholder approval.

2.  Service Plan.  Class A shareholders of the Fund will be asked to amend the
Fund's current Service Plan to permit payment of distribution fees, with no
change to the Plan's current limit on the total expenses payable.


To be attached to the cover page of the Prospectus of United Municipal High
Income Fund, Inc. Class A shares dated December 31, 1996.

This Supplement is dated May 29, 1997.

NUS1014B
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SUPPLEMENT TO THE PROSPECTUS

United Municipal High Income Fund, Inc. Class Y Shares

The following information supplements and supersedes any contrary information
contained in the Prospectus:

At a special meeting of shareholders scheduled for July 24, 1997, shareholders
of the Fund will be asked to approve proposals relating to elimination of or
changes to certain of the Fund's fundamental investment restrictions.  If
approved, the current fundamental restrictions regarding mortgaging or pledging
securities, arbitrage transactions, securities owned by affiliated persons and
options, futures contracts, forward currency contracts and other derivative
instruments would be eliminated.  Also, if approved, the current fundamental
restrictions regarding diversification, investments in commodities and commodity
contracts, loans, margin purchases and short sales would be modified.

If the foregoing changes to the Fund's fundamental investment restrictions are
approved, the Fund intends to implement new non-fundamental, operating policies
regarding derivative instruments and mortgaging or pledging securities.  These
operating policies would be in addition to the other non-fundamental
restrictions and policies set forth in the prospectus and Statement of
Additional Information and could be changed by the Board of Directors without
shareholder approval.

To be attached to the cover page of the Prospectus of United Municipal High
Income Fund, Inc. Class Y shares dated December 31, 1996.

This Supplement is dated May 29, 1997.

NUS1014-Y
<PAGE>
UNITED MUNICIPAL HIGH INCOME FUND, INC.

             Supplement to the Statement of Additional Information
                            Dated  December 31, 1996


The following information supplements and supersedes any contrary information
contained in the Statement of Additional Information:

1.  Investment Restrictions. At a special meeting of shareholders scheduled for
July 24, 1997 ("Special Meeting"), shareholders of the Fund will be asked to
approve elimination and modification of certain of the Fund's fundamental
investment restrictions.  If approved, the following investment restrictions
will supersede and replace the restrictions listed in the "Investment
Restrictions" section:

     The Fund:

       May not make any investments other than in the municipal bonds and in the
     taxable obligations, options, futures contracts and other financial
     instruments described in the Prospectus;

       May not purchase any voting securities; purchase or sell physical
     commodities; however, this policy shall not prevent the Fund from
     purchasing and selling foreign currency, futures contracts, options,
     forward contracts, swaps, caps, collars, floors and other financial
     instruments; or purchase any real estate or interests in real estate
     investment trusts;

     (iii)  May not lend money or other assets (neither purchasing debt
     securities and other obligations consistent with its goal and its other
     investment policies and restrictions or engaging in repurchase transactions
     is considered "lending");

       May not borrow money except that, as a temporary measure for
     extraordinary or emergency purposes and not for investment purposes, the
     Fund may borrow from banks up to 5% of the value of its total assets;

       May not invest for the purpose of exercising control or management of
     other companies;

       May not sell securities short (unless it owns or has the right to obtain
     securities equivalent in kind and amount to the securities sold short) or
     purchase securities on margin, except that (1) this policy does not prevent
     the Fund from entering into short positions in foreign currency, futures
     contracts, options, forward contracts, swaps, caps, collars, floors and
     other financial instruments, (2) the Fund may obtain such short-term
     credits as are necessary for the clearance of transactions, and (3) the
     Fund may make margin payments in connection with futures contracts,
     options, forward contracts, swaps, caps, collars, floors and other
     financial instruments;

       May not participate on a joint, or a joint and several, basis in any
     trading account in securities;

      May not engage in the underwriting of securities;

       With respect to 75% of its total assets, may not purchase securities of
     any one issuer (other than cash items and "Government securities" as
     defined in the Investment Company Act of 1940, as amended (the "1940
     Act")), if immediately after and as a result of such purchase, the value of
     the holdings of the Fund in the securities of such issuer exceeds 5% of
     the value of the Fund's total assets; or

       May not buy shares of other investment companies that redeem their
     shares.  The Fund may buy shares of investment companies that do not redeem
     their shares it if does so in a regular transaction in the open market and
     then does not have more than one-tenth (i.e., 10%) of its total assets in
     these shares.

     If the proposed changes to the Fund's fundamental investment restrictions
are approved, the Fund intends to implement the following new non-fundamental,
operating policies which would supersede and replace the Fund's current non-
fundamental restrictions and policies on these matters:

     (i)  Generally, the Fund may purchase and sell any type of derivative
     instrument (including, without limitation, futures contracts, options,
     forward contracts, swaps, caps, collars, floors and indexed securities).
     However, the Fund will only purchase or sell a particular derivative
     instrument if the Fund is authorized to invest in the type of asset by
     which the return on, or value of, the derivative instrument is primarily
     measured.

     (ii)  The Fund may not pledge its assets in connection with any permitted
     borrowings; however, this policy does not prevent the Fund from pledging
     its assets in connection with its purchase and sale of futures contracts,
     options, forward contracts, swaps, caps, collars, floors and other
     financial instruments.

2.  Service Plan.  Class A shareholders of the Fund will be asked to amend the
Fund's current Service Plan to permit payment of distribution fees, with no
change to the Plan's current limit on the total expenses payable.

This Supplement is dated May 29, 1997.



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