UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the
Securities Exchange Act of 1934

Filed by the Registrant   x

Filed by a Party other than the Registrant   o

Check the appropriate box:

o   Preliminary Proxy Statement

o   Confidential, for Use of the Commission Only (as permitted by Rule 14a-6(e)(2))

o   Definitive Proxy Statement

x   Definitive Additional Materials

o   Soliciting Material Pursuant to §240.14a-11(c) or §240.14a-12

Hallwood Realty Partners, L.P.

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement, if
other than the Registrant)

      Payment of Filing Fee (Check the appropriate box):

o   No fee required.

o   Fee computed on table below per Exchange Act Rules 14a-6(i)(1) and 0-11.

      1) Title of each class of securities to which transaction applies:

           Limited Partnership Units of Hallwood Realty Partners, L.P.

      2) Aggregate number of securities to which transaction applies: 1,593,948 units

      3) Per unit price or other underlying value of transaction computed pursuant to Exchange Act Rule 0-11 (set forth the amount on which the filing fee is calculated and state how it was determined):

      4) Proposed maximum aggregate value of transaction: $220,554,584.76

      5) Total fee paid: $27,994.27

      x   Fee paid previously with preliminary materials.

      o   Check box if any part of the fee is offset as provided by Exchange Act Rule 0-11(a)(2) and identify the filing for which the offsetting fee was paid previously. Identify the previous filing by registration statement number, or the Form or Schedule and the date of its filing.

      1) Amount Previously Paid:

      2) Form, Schedule or Registration Statement No.:

      3) Filing Party:

      4) Date Filed:

July 1, 2004

Dear Unitholder:

      Recently you received a proxy statement asking you to vote for approval of the merger of Hallwood Realty Partners, L.P. (the “Partnership”) with a wholly-owned subsidiary of HRPT Properties Trust (“HRPT”) pursuant to a merger agreement between the Partnership, HRPT and certain of their affiliates. As described in the proxy statement, a putative class action lawsuit was filed challenging certain actions taken by the Partnership, certain of its affiliates and the Board of Directors of Hallwood Realty, LLC, the general partner of the Partnership. The parties to that lawsuit have now entered into a Memorandum of Understanding reflecting an agreement in principle to settle the lawsuit. As part of that process, we agreed to provide the attached supplemental information concerning the merger and the Partnership. Please note that there have been no changes in the terms of the merger transaction itself.

      We have enclosed with this supplement an additional proxy card representing the units you own. If you have not yet voted or wish to change your vote, please execute the enclosed card to ensure that your units will be voted at the special meeting of unitholders, to be held on July 15, 2004. If you have already voted and do not wish to change your vote, no further action is required on your part. Please call our information agent, MacKenzie Partners, Inc. at (212) 929-5405 if you need additional information or have any questions.

      On behalf of the Board of Directors of Hallwood Realty, I thank you for your support and urge you to vote FOR approval and adoption of the merger agreement and the merger. We look forward to seeing you at the special meeting.

Sincerely,

ANTHONY J. GUMBINER

Chairman of the Board of Hallwood Realty, LLC

This proxy statement supplement is first being mailed to unitholders on or about July 1, 2004.

      This is a supplement to the proxy statement, dated June 15, 2004, relating to the special meeting of unitholders of Hallwood Realty Partners, L.P. (the “Partnership”), to be held at 10:00 a.m. Central Daylight Time, on July 15, 2004, at the offices of the Partnership, at 3710 Rawlins, Suite 1500, Dallas, Texas 75219. This supplement is being provided to advise you of certain additional information concerning the merger and the Partnership. Please note that there are no changes in the terms of the merger transaction. Terms defined in the original proxy statement are used with the same meaning in this supplement.

The Proposed Settlement

      As described in detail in the proxy statement, in April 2003, IG Holdings and certain other parties filed a putative class action lawsuit on behalf of the unitholders against the Partnership, the general partner and the then members of the Board in connection with the High River tender offer. The class plaintiffs later amended their complaint to add Mr. Schrauff and Hallwood Group as defendants. On June 30, 2004, the parties to the lawsuit entered into a Memorandum of Understanding setting forth the parties’ agreement in principle to settle the lawsuit.

      Under the terms of the proposed settlement, the parties have agreed that counsel for the class plaintiffs will request and the defendants will not object to counsel for the class plaintiffs receiving attorneys’ fees and expenses in the amount of approximately $2,500,000. The first $2,000,000 of any amount awarded by the Court of Chancery will be paid by the defendants’ insurer. Any remaining amount awarded by the Court will be withheld from the merger consideration to be received by the unitholders (including Hallwood Group), on a pro rata basis based on the number of units held, as more fully described in the proxy statement. The actual amount of fees and expenses to be paid to class counsel will be determined by the Court. If the Court determines to award $2,500,000 in fees and expenses, an amount equal to approximately $0.31 per unit would be withheld with respect to those fees and expenses.

      In connection with the proposed settlement, the Partnership has also agreed to provide the supplemental information concerning the merger and the Partnership contained in this proxy statement supplement.

      The Memorandum of Understanding also provides for certain further confirmatory discovery by the plaintiffs which will proceed promptly. The parties to the action will attempt in good faith to agree upon and execute as soon as practicable a Stipulation of Settlement of all the claims asserted in the action, providing for the certification of a class of unitholders and the dismissal with prejudice and release of all claims that were asserted or could have been asserted by such class in the action, and requiring the parties to use their best efforts to obtain final approval of the settlement from the Court.

      If the merger is not completed or the Court does not approve the settlement, the Memorandum of Understanding will be null and void. It is possible that the Court will not rule on the settlement for several months following completion of the merger.

      The defendants, including the Partnership and the Board, continue to deny any wrongdoing and have entered into the proposed settlement to eliminate the burden, expense and distraction of further litigation and to permit the merger to proceed without risk of injunctive or other relief.

Description of the Merger

      After taking into account the adjustments described in detail in the proxy statement, unitholders will receive approximately $136.16, subject to the further adjustments described in the proxy statement. Prior to the adjustments to the $250 million aggregate consideration pursuant to the terms of the merger agreement and the purchase agreement, unitholders would have received $138.47 per unit, subject to adjustment (rather than $136.16, as described on page 11 of the proxy statement).

Background of the Merger

      The following is additional information regarding the background of the proposed merger and should be read in conjunction with the more complete information appearing in the original proxy statement under the heading “Background of the Merger.”

      At the Board meeting held on May 13, 2003, Morgan Stanley presented to the Board Morgan Stanley’s financial analyses of the High River tender offer and Morgan Stanley’s opinion that the $100 per unit offered in the tender offer was inadequate from a financial point of view to the holders of the units (other than High River and its affiliates). The Board did not at that time, however, request that Morgan Stanley consider or advise the Board of alternatives to the tender offer. Also at that meeting, Morgan Stanley noted that its analysis of the value of the Partnership was based in part on comparisons to office and industrial real estate investment trusts, rather than partnerships, and that certain characteristics of the Partnership would require changes in order for the Partnership to be valued in the same range as those companies. Consequently, Morgan Stanley expressed its view that, absent a sale or similar transaction involving the Partnership, if certain of those characteristics did not change, the units would likely trade lower than the comparable companies’ trading values and lower than the then-current trading price of the units. Morgan Stanley’s analyses of the implied value of the units at that meeting were based on an allocation of 99% of the total value to the limited partners and 1% to the general partner.

      On August 22, 2003, High River sent a letter to Morgan Stanley outlining High River’s position with respect to participating in Morgan Stanley’s marketing process. In that letter, High River indicated that High River would be willing to sign an agreement including confidentiality and standstill provisions so that it could conduct due diligence with respect to the Partnership, if the Partnership and the general partner would enter into a binding agreement with High River to sell the Partnership by a date certain to the highest bidder.

      On October 1, 2003, the audit committee met to discuss retaining outside legal counsel and a financial advisor to assist it with its negotiations with Hallwood Group with respect to the negotiation of the allocation of the transaction consideration between the unitholders (other than Hallwood Group and its affiliates), on the one hand, and the various interests in the Partnership held by Hallwood Group, including the general partner interest, on the other hand. The audit committee determined to retain Prickett, Jones and Elliott, P.A. as its outside legal counsel and considered Lehman Brothers and two other candidates for purposes of providing financial advisory services to the audit committee. On October 2, 2003, the audit committee’s counsel informed the Board that the audit committee had decided to engage one of the other candidates as its financial adviser. Representatives of that candidate attended the audit committee meeting on October 3, 2003. That candidate proposed a fee in connection with its services to the audit committee of $1,500,000.

      With respect to the trial held on October 7 and 8, 2003, the class plaintiffs sought an order of the Court (1) declaring that the defendants had breached their contractual and fiduciary duties to the unitholders and the Partnership; (2) requiring the defendants to take action to redeem the rights under the Partnership’s rights plan or otherwise render the Partnership’s rights plan inapplicable to the tender offer and to disclose all material information to the unitholders in order that the unitholders would have adequate information to make a decision with respect to the revised tender offer (a) immediately if no bona fide indications of interest in a transaction with the Partnership were received on or before September 30, 2003, or (b) on or before November 7, 2003, if one or more bona fide indications of interest in such an acquisition were received on or before September 30, 2003; and (3) granting such other relief as the Court deemed just and proper. High River sought an order of the Court (i) declaring that the defendants had breached their contractual and fiduciary duties to the Partnership and its unitholders, (ii) directing the defendants to carry out their duties to High River and the other unitholders of the Partnership by terminating the rights plan and taking any further action necessary to allow the unitholders of the Partnership to freely consider the revised tender offer, (iii) awarding High River its costs and expenses, including reasonable attorneys’ fees, and (iv) granting High River such other and further relief as the Court may deem just and proper. At the conclusion of the trial, the Delaware Court of Chancery

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did not grant any of the requested relief and instead deferred decision. During the period from October 16, 2003 through May 3, 2004, the Court ordered nine status conferences and related discovery and information to be provided by the defendants to the class plaintiffs and High River regarding the status of the sale process and the negotiations of the allocation of the merger consideration.

      At an audit committee meeting on October 9, 2003, the audit committee discussed with the candidate that it was considering retaining as its financial advisor that, as had previously been discussed with the candidate, the financial advisor to the audit committee would be expected to opine on the reasonableness of the allocation of the total transaction consideration between the holders of the limited partnership interests and the holders of the general partnership interests. Representatives of the candidate subsequently advised the audit committee’s outside legal counsel that, because its internal policies precluded such opinions, the candidate would not agree to opine as to the reasonableness of the allocation of consideration in a transaction such as the merger and withdrew from consideration as the audit committee’s financial advisor. The audit committee then determined to engage Lehman Brothers as its financial advisor.

      Also at the October 9, 2003 meeting, Morgan Stanley updated the audit committee on the status of the bids received to date. Morgan Stanley informed the audit committee that it had received proposals from six bidders, who had proposed nominal total consideration ranging from $239 million to $276 million.

      At the November 14, 2003 Board meeting, representatives of Morgan Stanley updated the Board on the status of the second round of bid proposals it had received. Morgan Stanley noted that second round proposals had been received from four bidders. Three of the bidders had reduced their bids and proposed nominal total consideration ranging from $201 million to $227 million. Another bidder increased its bid to a nominal consideration of $263 million, but had not supplied information requested by Morgan Stanley to enable Morgan Stanley to determine whether that bidder would be able to complete a transaction, including information regarding the proposed transaction structure, the bidder’s ability to obtain funds to complete a transaction and the amount of due diligence required to be conducted by that bidder. Morgan Stanley also noted that the other bidders that had previously submitted proposals had not submitted second bids. The three bidders submitting the reduced bids attributed the reduction in their bids to various factors, including declining occupancies at certain properties, softening asking rents at other properties, generally lower projected occupancies and higher expected real estate taxes.

      Between November 5, 2003 and April 14, 2004, negotiations between the audit committee and Hallwood Group continued with respect to the allocation of the total merger consideration between the unitholders (other than the general partner and its affiliates) on the one hand, and the general partner and its affiliates, on the other hand. On January 6, 2004, in the course of reviewing the status of discussions regarding the allocation of consideration, Lehman Brothers advised the audit committee that Lehman Brothers anticipated that, if ever asked to do so, it would have difficulty rendering an opinion that an allocation resulting in the limited partners receiving only $125.00 per unit would be reasonable in light of the amount of total consideration then being proposed.

      During February 2004, the exclusivity period that the Partnership had granted to one of the primary bidders expired. The Board determined to extend the exclusivity period with that bidder and on March 2, 2004, the exclusivity period was extended to March 15, 2004. The letter from the Partnership to that bidder agreeing to extend the exclusivity period specified that at the time of signing any definitive agreement, the bidder must have received signed commitments for the financing of the transaction, that such commitments would contain customary “market out” provisions and that, if the transaction was terminated due to such “market out” provisions, the bidder would be required to pay the Partnership a termination fee of either $10 million or $20 million, depending upon the circumstances of the termination. When the exclusivity period with that bidder expired on March 15, 2004, the Partnership refused the bidder’s request to extend the exclusivity period further and instead resumed discussions with HRPT.

      At the April 15, 2004 Board meeting, in connection with its presentation to the Board of its financial analyses relating to the proposed transaction and the delivery of its opinion with respect to the fairness of the total merger consideration, as each is described in the proxy statement, Morgan Stanley noted that, although its prior opinions concerning the inadequacy of the price offered by High River had been based

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on value on a per unit basis, Morgan Stanley’s opinion to the Board at the April 15 meeting addressed only the total consideration to be paid with respect to the Partnership as a whole, including all of the units.

Opinion of Morgan Stanley

      In addition to the factors and analyses discussed in the proxy statement, in discussing its analyses of the fairness of the total merger consideration with the Board:

•  Morgan Stanley noted that the characteristics of the Partnership that were not similar to certain characteristics of the companies used in Morgan Stanley’s analyses would likely result in the units trading at lower valuations than those companies and lower than the then-current trading price of the units in the absence of a sale or other transaction involving the Partnership, unless those characteristics were to changed to make them similar; and

•  Morgan Stanley noted that its “Comparable Companies Analysis” did not include any limited partnerships as a basis of comparison.

Interests in the Merger that Differ from Your Interests

      Clarification is made with respect to the discussion of severance payments to be made to certain officers and key employees of the general partner and HCRE. Specifically, Mr. Gumbiner, a member of the Board and an executive officer of the general partner, HCRE and Hallwood Group, is not receiving any severance payments or bonuses in connection with the merger.

The Purchase Agreement

Sale of General Partner Interest; Units

      The sale of the general partner interest requires that the Partnership take certain actions under the partnership agreement, such as obtaining certain opinions of counsel as to the tax effects of the merger. In addition, Successor GP will be required to agree to become the successor general partner in writing.

Recommendation of the Board

      The Board, taking into account the opinion of its independent financial advisor, Morgan Stanley, regarding the total amount of transaction consideration to be received, and the recommendation of the audit committee of the Board, which had received the opinions of Lehman Brothers Inc. regarding the fairness of the consideration to be received by unitholders and the reasonableness of the allocation of the consideration, has unanimously determined that the merger is fair to, and in the best interests of, the Partnership and its unitholders, recommends the merger and recommends that you vote FOR approval and adoption of the merger agreement and the merger.

      If you have not yet voted or wish to change your vote, please execute the enclosed card to ensure that your units will be voted at the special meeting of unitholders, to be held on July 15, 2004. If you have already voted and do not wish to change your vote, no further action is required on your part. Please call our information agent, MacKenzie Partners, Inc. at (212) 929-5405, if you need additional information or have any questions.

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