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                                                                       EXHIBIT 7


                               September 24, 2001
                                  Supplement to
                           Offer to Purchase for Cash

                             AIMCO PROPERTIES, L.P.
              is offering to purchase limited partnership units in
                       UNITED INVESTORS INCOME PROPERTIES
                                       for
                            $120.40 PER UNIT IN CASH
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     YOUR RIGHTS TO TENDER AND WITHDRAW YOUR UNITS WILL EXPIRE AT 5:00 P.M.,
                        NEW YORK TIME, ON OCTOBER 2, 2001
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On September 4, 2001, we offered to purchase the limited partnership units of
United Investors Income Properties upon the terms and subject to the conditions
of the offer to purchase of that date. This notice supplements the information
contained in the original offer to purchase. We are using the same defined terms
in this Supplement that we used in the original offer to purchase.

PLEASE READ THE OFFER TO PURCHASE, TOGETHER WITH THIS SUPPLEMENT, FOR A
DESCRIPTION OF OUR OFFER. QUESTIONS AND REQUESTS FOR ADDITIONAL COPIES OF THE
OFFER TO PURCHASE, THE AMENDED ACKNOWLEDGMENT AND AGREEMENT, OR THE LETTER OF
TRANSMITTAL MAY BE DIRECTED TO THE INFORMATION AGENT AT (888) 349-2005.

Please take note of the following clarifications and supplements of the offer to
purchase:

WAIVER OF CONDITIONS

Our original offer to purchase provides that we will not be required to accept
for payment and pay for units if, among other things, the following shall occur
or may be reasonably expected to occur at or prior to the expiration of our
offer:

         1.   any general suspension of trading in, or limitation on prices for,
              securities on any national securities exchange or the
              over-the-counter market in the United States;

         2.   a decline in the closing price of a Share of AIMCO's Class A
              Common Stock of more than 5.0% from the date of the initial offer
              (September 4, 2001);

         3.   any extraordinary or material adverse change in the financial,
              real estate or money markets or major equity security indices in
              the United States such that there shall have occurred at least a
              25 basis point increase in LIBOR, or at least a 5.0% decrease in
              the price of the 10-year Treasury Bond or the 30-year Treasury
              Bond, or at least a 5.0% decrease in the S&P 500 Index or the
              Morgan Stanley REIT Index, in each case from the date of the
              initial offer (September 4, 2001); or

         4.   a commencement of a war, conflict, armed hostilities or other
              national or international calamity directly or indirectly
              involving the United States, not existing as of the date of the
              initial offer (September 4, 2001).

The terrorist attacks in New York and Washington, DC on September 11, 2001 and
related events, including the subsequent closing of the markets in the United
States and the significant decline in market indices when trading resumed on
September 17, 2001, triggered the conditions set forth above. Despite these
events, we have decided to waive each of these conditions and are hereby
notifying you of our waiver so that we may proceed with our offer.

ADDITIONAL CONDITIONS

Please be aware, however, that our offer remains subject to each and every
condition in the offer to purchase that we have not specifically waived as set
forth above, and to each of the following new conditions: