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

                                   -----------

                                    FORM 8-K

                                 CURRENT REPORT
                     PURSUANT TO SECTION 13 OR 15(D) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

         Date of Report (Date of Earliest Event Reported): May 23, 2005

                                GERON CORPORATION
             (Exact name of registrant as specified in its charter)

         Delaware                      0-20859                  75-2287752
(State or other jurisdiction   (Commission File Number)       (IRS Employer
      of incorporation)                                     Identification No.)


                             230 CONSTITUTION DRIVE
                          MENLO PARK, CALIFORNIA 94025
          (Address of principal executive offices, including zip code)

                                 (650) 473-7700
              (Registrant's telephone number, including area code)

                                       N/A
          (Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to
simultaneously satisfy the filing obligation of the registrant under any of the
following provisions (see General Instruction A.2. below):

[ ] Written communications pursuant to Rule 425 under the Securities Act (17 CFR
    230.425)

[ ] Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 
    240.14a-12)

[ ] Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange
    Act (17 CFR 240.14d-2(b))

[ ] Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange
    Act (17 CFR 240.13e-4(c))




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Item 8.01                  Other Events.

The Company deems the following information to be material:

     On May 23, 2005, the Company announced that it had received clearance from
the U.S. Food and Drug Administration (FDA) to initiate clinical testing of its
lead anti-cancer compound, GRN163L, in patients with chronic lymphocytic
leukemia (CLL). The company filed its first Investigational New Drug Application
(IND) for GRN163L in April 2005.

     The Company's Press Release, dated May 23, 2005, is attached hereto as
Exhibit 99.1 and is incorporated herein by reference.

Item 9.01.    Financial Statements and Exhibits

              (a) Financial Statements.

                       None.

              (b) Pro Forma Financial Information

                       None.

              (c) Exhibits:

                       99.1    Press Release of Geron Corporation, dated May 23,
                               2005.




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                                   SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned hereunto duly authorized.


                                      GERON CORPORATION



Date: May 23, 2005                    By: /s/ David L. Greenwood         
                                          --------------------------------
                                              David L. Greenwood
                                              Executive Vice President and Chief
                                              Financial Officer




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