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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): April 28, 2004


                                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 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 April 28, 2004, Geron Corporation, a Delaware corporation (the "Company"),
announced that Kirin Brewery Co., Ltd. has filed a lawsuit against Geron in the
U.S. District Court for the Northern District of California. The lawsuit alleges
interference with contract and interference with Kirin's prospective business
advantage in connection with Geron's recent acquisition of rights from Merix
Bioscience, Inc. for the development of cancer vaccines.

The Company's press release announcing the lawsuit is filed as an exhibit to
this Current Report on Form 8-K. The summary description of the lawsuit 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 April 28, 2004







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                                    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:    April 28, 2004              By:      /s/ William D. Stempel
                                              ----------------------------------
                                     Name:    William D. Stempel
                                     Title:   Vice President and General Counsel




                                  EXHIBIT INDEX

Exhibits

99.1                Press release dated April 28, 2004








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