SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                                   SCHEDULE TO

            Tender Offer Statement under Section 14(d)(1) or 13(e)(1)
                     of the Securities Exchange Act of 1934

                                (Amendment No. 4)

                         Shelbourne Properties III, Inc.
                         -------------------------------
                       (Name of Subject Company (Issuer))

                               HX Investors, L.P.
                               ------------------
                 (Names of Filing Persons (identifying status as
                        offeror, issuer or other person))

                     Common Stock, par value $0.01 per share
                     ---------------------------------------
                         (Title of Class of Securities)

                                    82137E103
                                    ---------
                      (CUSIP Number of Class of Securities)

                                Michael L. Ashner
                               HX Investors, L.P.
                        100 Jericho Quadrangle, Suite 214
                             Jericho, New York 11753
                                  516-822-0022

      (Name, address, and telephone numbers of person authorized to receive
             notices and communications on behalf of filing persons)

                                   Copies to:

                                 Justin P. Klein
                     Ballard Spahr Andrews & Ingersoll, LLP
                         1735 Market Street, 51st Floor
                        Philadelphia, Pennsylvania 19103
                                  215-864-8606


                            Calculation of Filing Fee
--------------------------------------------------------------------------------
    Transaction valuation                     Amount of Filing Fee
--------------------------------------------------------------------------------
        $12,896,389.50                              $1,186.47
--------------------------------------------------------------------------------



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

     Amount Previously Paid: $1,066.73

     Form or Registration No.: Schedule TO (Amendment No. 1)

     Filing Party: HX Investors, L.P.

     Date Filed: July 5, 2002

     [ ] Check the box if the filing relates solely to preliminary
communications made before the commencement of a tender offer.

     Check the appropriate boxes below to designate any transactions to which
the statement relates:

     [X] third-party tender offer subject to Rule 14d-1.

     [ ] issuer tender offer subject to Rule 13e-4.

     [ ] going-private transaction subject to Rule 13e-3.

     [ ] amendment to Schedule 13D under Rule 13d-2.

     Check the following box if the filing is a final amendment reporting the
results of the tender offer: [ ]





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                                  TENDER OFFER

     This Amendment No. 4 amends the Tender Offer Statement on Schedule TO (the
"Statement") filed with the Securities and Exchange Commission on July 5, 2002
by HX Investors, L.P., a Delaware limited partnership (the "Purchaser") to
purchase up to 236,631 shares of Common Stock of Shelbourne Properties III, Inc.
(the "Company"), upon the terms and subject to the conditions set forth in the
Offer to Purchase dated July 5, 2002 (the "Offer to Purchase") and the related
Letter of Transmittal, copies of which were attached thereto as Exhibits (a)(1)
and (a)(2), respectively.

     The information in the Supplement to Offer to Purchase dated August 1,
2002, is hereby expressly incorporated herein by reference.

     Item 12. Exhibits.

         Item 12 is hereby amended by adding the following Exhibits which are
filed herewith

     Exhibit No.  Exhibit
     -----------  -------

     (a)(11)      Supplement to Offer to Purchase dated August 1, 2002.

     (a)(12)      Press Release issued August 1, 2002.

     (d)(3)       Letter to the Boards of Directors of Shelbourne Properties I,
                  Inc., Shelbourne Properties II, Inc. and Shelbourne
                  Properties III, Inc.



                                    SIGNATURE

     After due inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.

                                            HX INVESTORS, L.P.

                                            By: Exeter Capital Corporation
                                                General Partner

                                                By: /s/ Carolyn Tiffany
                                                    ----------------------------
                                                        Carolyn Tiffany
                                                        Vice President

Dated: August 1, 2002





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                                  EXHIBIT INDEX


    Exhibit No.   Description
    -----------   -----------

     (a)(11)      Supplement to Offer to Purchase dated August 1, 2002.

     (a)(12)      Press Release issued August 1, 2002.

     (d)(3)       Letter to the Boards of Directors of Shelbourne Properties I,
                  Inc., Shelbourne Properties II, Inc. and Shelbourne
                  Properties III, Inc.



















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