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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT
                     Pursuant to Section 13 or 15(d) of the
                       SECURITIES AND EXCHANGE ACT OF 1934

         Date of Report (Date of earliest event reported): June 30, 2004


                                GERON CORPORATION


             (Exact name of registrant as specified in its charter)

          Delaware                   0-20859                    75-2287752
(State or Other Jurisdiction      (Commission                (IRS Employer
      of Incorporation)            File Number)           Identification Number)

          230 Constitution Drive                                   94025
          Menlo Park, California                                 (Zip Code)
 (Address of principal executive offices)



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

                                       N/A
          (Former Name or Former Address, if Changed Since Last Report)






Item 5.  Other Events.

On June 30, 2004, Geron Corporation, a Delaware corporation (the "Company"), and
Kyowa Hakko Kogyo Co., Ltd. announced that Kyowa Hakko has returned Asian
territory development and marketing rights for Geron's telomerase inhibitors.

The Company's press release announcing the conclusion of the collaboration is
filed as an exhibit to this Current Report on Form 8-K. The summary description
of the transaction and the press release are qualified in their entirety by
reference to the document filed as an exhibit hereto.

Item 7.  Exhibits.

Exhibits
--------

99.1                Press release dated June 30, 2004



                                    SIGNATURE


     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:    June 30, 2004                          By: /s/ William D. Stempel
                                                    ----------------------------
                                                Name:   William D. Stempel
                                                Title:  Vice President and
                                                General Counsel


                                  EXHIBIT INDEX

Exhibits
--------

99.1                Press release dated June 30, 2004