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 2, 2003


                                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 June 2, 2003, Geron Corporation, a Delaware corporation (the "Company"),
entered into a License Amendment Agreement (the "Amendment") with Transgenomic,
Inc., a Delaware corporation ("Transgenomic"), to amend an existing license
agreement between the parties. As part of the consideration for the amendment to
the License Agreement, Transgenomic agreed to purchase 310,000 shares of Geron
common stock, at $5.05 per share, the Nasdaq closing price on June 2, 2003.
The terms and conditions of the stock purchase are set forth in a Stock Purchase
Agreement, dated June 2, 2003 (the "Stock Purchase Agreement").

The Company's press release announcing the Amendment, as well as the Stock
Purchase Agreement, are filed as exhibits 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 documents filed as exhibits hereto.

Item 7.    Exhibits.

Exhibits
--------

4.1        Stock Purchase Agreement dated as of June 2, 2003, by and
           between Registrant and Transgenomic, Inc.
99.1       Press Release dated June 4, 2003









                                   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:      June 4, 2003             By:   /s/ William D. Stempel
                                        ----------------------------------------
                                    Name:     William D. Stempel
                                    Title:    Vice President and General Counsel


                                  EXHIBIT INDEX


Exhibits
--------

4.1             Stock Purchase Agreement dated as of June 2, 2003, by and
                between Registrant and Transgenomic, Inc.
99.1            Press Release dated June 4, 2003