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                                                                   EXHIBIT 10.18


                    Hines-Sumisei U.S. Core Office Fund, L.P.
                       2800 Post Oak Boulevard, Suite 5000
                              Houston, Texas 77056





June 3, 2004






Hines US Core Office Capital LLC
Hines US Core Office Capital Associates II Limited Partnership
Hines REIT Properties, L.P.
2800 Post Oak Boulevard, Suite 5000
Houston, Texas  77056


         Re:      Rights of Hines REIT Properties, L.P.
                  to acquire an interest and invest in
                  Hines-Sumisei U.S. Core Office Fund, L.P.

Ladies and Gentlemen:

                  The purpose of this letter agreement is to document the rights
of Hines REIT Properties, L.P. (together with any wholly-owned subsidiary
thereof, the "Public REIT OP"), a Delaware limited partnership, to acquire an
interest in and to participate in future offerings of Hines-Sumisei U.S. Core
Office Fund, L.P. (the "Partnership"), a Delaware limited partnership.
Capitalized terms used and not otherwise defined herein have the meanings given
to them in the Third Amended and Restated Agreement of Limited Partnership,
dated April 23, 2004, of the Partnership (such agreement, as amended from time
to time, the "Partnership Agreement").

                  For good and valuable consideration, the receipt and
sufficiency which are hereby acknowledged, the parties hereto agree as follows:

INITIAL PURCHASE RIGHT

                  The Public REIT OP shall have the right and obligation (the
"Initial Investment Right") to acquire up to 35,000 of the Partnership Units
(the "Reserved Units") held by Hines US Core Office Capital Associates II
Limited Partnership (the "Hines Limited Partner") at a price per Unit equal to
the Initial Offering Price. To the extent the Public REIT OP receives net
proceeds from the public offering of common shares contemplated by Hines Real
Estate Investment Trust, Inc. or contributed to the Public REIT OP by Hines Real
Estate Holdings Limited Partnership ("Net Proceeds"), the Public REIT OP shall
use all such Net Proceeds (up to $35 million) to acquire the Reserved Units. The
Public REIT OP may acquire the Reserved Units in one or more installments of not
less than $100,000 (or such lesser amount as the Hines Limited Partner may
accept) as Net Proceeds become available. The Public REIT OP's right and
obligation to acquire the Reserved Units shall terminate on the first
anniversary of the date the registration statement filed by Hines Real Estate
Investment Trust, Inc. is declared effective by the Securities and Exchange
Commission. The Hines Limited Partner shall at all times prior to such date
maintain ownership of at least 35,000 Units plus such additional number of Units
as shall be necessary, taken together with other interests in the Fund held by
Affiliates of Hines, to ensure that the Hines Capital Requirement remains
satisfied following the transfer of the Reserved Units to the Public REIT OP.


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                  The sale of any portion of the Reserved Units shall be
conditioned upon (1) the Public REIT OP receiving Net Proceeds and (ii) the
satisfaction of the conditions to the transfer of a Partnership Interest set
forth in Sections 10.5 and 10.6 of the Partnership Agreement.

                  Upon the delivery of any Net Proceeds to the Hines Limited
Partner as contemplated above, the following shall take place:

                  1.       The Public REIT OP shall deliver to the Partnership
                           such documentation as the General Partner reasonably
                           requires to verify the satisfaction of the conditions
                           to transfer set forth in Section 10.5 of the
                           Partnership Agreement;

                  2.       The Public REIT OP shall deliver the applicable Net
                           Proceeds to the Hines Limited Partner by wire
                           transfer of immediately available funds to an account
                           designated by the Hines Limited Partner;

                  3.       The Units associated with the portion of the Reserved
                           Units being acquired by the Public REIT OP
                           (determined by dividing the applicable Net Proceeds
                           delivered by the Initial Offering Price) shall be
                           transferred on the books of the Partnership to the
                           Public REIT OP;

                  4.       The Public REIT OP shall be admitted to the
                           Partnership as a Non-Managing General Partner as
                           contemplated by Section 5.11 of the Partnership
                           Agreement and all Units transferred to it shall
                           automatically be deemed to be held by it in respect
                           of its non-managing general partner interest in the
                           Partnership; and

                  5.       The General Partner shall amend the Partnership
                           Agreement to the extent necessary to give effect to
                           the foregoing in accordance with the terms of the
                           Partnership Agreement, it being understood that the
                           Public REIT OP will hold only a non-managing general
                           partner interest in the Partnership unless the
                           General Partner and the Public REIT OP otherwise
                           agree (subject to the terms of the Partnership
                           Agreement).

Pre-Emptive Right

                  Following the Initial Offering Period, for so long as the
Public REIT OP is a partner in the Partnership, the Partnership shall give the
Public REIT OP written notice (an "Offer Notice") of any proposed offering by
the Partnership of additional Units for cash at least 90 days prior to the
anticipated closing date of such offering, which notice shall specify the total
number of Units being offered and the price per Unit at which the Partnership is
offering Units in such offering. The Public REIT OP shall have the right (a
"Preemptive Right") to acquire up to 40% of the Units sold by the Partnership in
any such offering; provided that all Units issued to the Public REIT OP shall be
issued in respect of its non-managing general partner interest in the
Partnership, notwithstanding that Units may otherwise be offered in such
offering in respect of limited partner interests in the Partnership. In order to
exercise its Pre-Emptive Right, the Public REIT OP must deliver a written notice
(an "Exercise Notice") to the Partnership and the General Partner within 30 days
after delivery of the Offer Notice, which Exercise Notice must specify the total
number of Units the Public REIT OP wishes to acquire, up to 40% of the total
number of Units issued in such offering. If the Public REIT OP delivers an
Exercise Notice within such 30 day period, then the Public REIT OP will be
obligated to buy, and the Partnership shall be obligated to sell to the Public
REIT OP, that number of Units specified in the Exercise Notice, up to 40% of the
total number of Units issued in such offering; provided that the Partnership
shall have no obligation to sell any Units to the Public REIT OP if such
offering is cancelled.

Miscellaneous

                  This letter agreement shall be governed by the laws of the
State of New York. This letter agreement may be signed in multiple counterparts,
which, taken together, shall constitute one and the same agreement.



                            [Signature pages follow.]


                                       2
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                  Please indicate your agreement with the foregoing by signing
below.


                                Very truly yours,

                                HINES-SUMISEI U.S. CORE OFFICE FUND, L.P.

                                   By:  Hines US Core Office Capital LLC

                                        By:  Hines Interests Limited Partnership

                                             By:  Hines Holdings, Inc.



                                             By:  /s/ CHARLES N. HAZEN
                                                --------------------------------
                                                Name: Charles N. Hazen
                                                Title: Senior Vice President
AGREED:


HINES US CORE OFFICE CAPITAL LLC


          By:  Hines Interests Limited Partnership

               By:  Hines Holdings, Inc.



               By: /s/ CHARLES N. HAZEN
                  --------------------------------------------
                  Name: Charles N. Hazen
                  Title: Senior Vice President



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Hines US CORE OFFICE CAPITAL ASSOCIATES II LIMITED PARTNERSHIP

     By:  Hines US Core Office Capital LLC

          By:  Hines Interests Limited Partnership

               By:  Hines Holdings, Inc.



               By: /s/ CHARLES N. HAZEN
                  --------------------------------------------
                  Name: Charles N. Hazen
                  Title: Senior Vice President



HINES REIT PROPERTIES, L.P.

               By:  Hines Real Estate Investment Trust, Inc.



          By: /s/ SHERRI W. SCHUGART
             -------------------------------------------------
             Name: Sherri W. Schugart
             Title: Chief Financial Officer