Exhibit 99.1

Geron Corporation Reports 2005 First Quarter Financial Results and Events

    MENLO PARK, Calif.--(BUSINESS WIRE)--April 29, 2005--Geron
Corporation (Nasdaq:GERN) today reported financial results for the
three months ended March 31, 2005.
    For the first quarter of 2005, the company reported operating
revenue of $59,000 and operating expenses of $10.4 million compared to
$248,000 and $52.3 million, respectively, for the comparable period in
2004. Net loss for the period was $9.7 million or $(0.18) per share
compared to $51.7 million or $(1.28) per share for the comparable
period in 2004.
    Operating expenses for the first quarter of 2004 included a
non-cash charge of $45.2 million related to the acquisition of
technology rights from Merix Bioscience, Inc. (now Argos
Therapeutics). Excluding that charge, the company's overall research
and development expenses increased in the first quarter of 2005 as a
result of higher personnel-related costs and increased consulting
costs for clinical and regulatory matters. The increase in the
company's general and administrative expenses for 2005 was primarily
due to a non-cash charge for the fair value of a warrant issued to a
consultant.
    The company expects its research and development expenses to
increase in the future as it continues clinical manufacturing and
testing of its telomerase inhibitor compounds, furthers the
development of its human embryonic stem cell programs and expands its
activities in the development of telomerase-based cancer vaccines.
    Revenues for the first quarter of 2005 and 2004 represented
royalty revenues under various license agreements with companies for
sales of telomerase-based diagnostic kits, shared profits from sales
of reagent research products, and license fee revenues recognized from
sublicense agreements or license option agreements with various
companies for nuclear transfer and telomerase technology.

    First Quarter 2005 Highlights:

    --  The Board of Patent Appeals and Interferences of the U.S.
        Patent and Trademark Office issued a final judgment ending
        patent interference number 104,746 between Geron and Advanced
        Cell Technology Corporation (ACT) of Worcester, Mass., having
        to do with claims related to nuclear transfer technology. The
        Board ended the interference by entering judgment against ACT
        on all counts in the priority phase of the interference,
        thereby invalidating U.S. Patent No. 5,945,577, which is
        licensed to ACT from the University of Massachusetts.

    --  Geron Corporation granted a worldwide license to Cambrex
        (NYSE:CBM) under which a Cambrex subsidiary will develop and
        distribute cell lines that have been immortalized using
        Geron's proprietary telomerase technology.

    --  Geron received proceeds of $12.5 million upon the exercise of
        warrants to purchase approximately 2.0 million shares of
        common stock. The warrants were issued to institutional
        investors in connection with the financing announced in
        November 2004 and had an expiration date of January 11, 2005.

    --  The Board of Patent Appeals and Interferences of the U.S.
        Patent and Trademark Office issued a final judgment in
        interference number 105,192 between Geron and ACT, having to
        do with claims related to nuclear transfer technology. In its
        ruling, the Board found all claims of U.S. Patent No.
        6,235,970, which is licensed to ACT from the University of
        Massachusetts, to be unpatentable, effectively invalidating
        the patent.

    --  Geron and the Biotechnology Research Corporation (BRC) of Hong
        Kong formed a new company, TA Therapeutics, Limited (TAT), in
        Hong Kong. TAT will conduct research and develop telomerase
        activator drugs to restore the functional capacity of cells in
        various organ systems that have been impacted by senescence,
        injury or chronic disease.

    --  The Journal of Immunology published results of a completed
        Phase 1-2 clinical trial of Geron's telomerase therapeutic
        vaccine administered to patients with metastatic prostate
        cancer at Duke University Medical Center. The results showed
        that the vaccination protocol successfully generated
        telomerase-specific T-cell responses in 19 of 20 subjects. The
        vaccine was well tolerated with no major treatment-related
        toxicities.

    --  Geron's collaborators presented studies showing that small
        molecule telomerase activators, GRN139951 and GRN140665,
        enhanced the functional activity of immune cells from HIV/AIDS
        donors. The research demonstrated that the Geron compounds
        increased the proliferative capacity of cytotoxic T-cells and
        their ability to produce a virus-fighting molecule, gamma
        Interferon.

    --  Stem Cells published Geron studies which demonstrated that
        human embryonic stem cells (hESCs) can be propagated in
        culture using defined growth factors without the need for
        feeder cells or media conditioned by feeder cells. The results
        represented a major step forward in the development of
        scalable systems to culture hESCs for the production of
        therapeutic cell products.

    Geron is a biopharmaceutical company developing and
commercializing three groups of products: i) therapeutic products for
oncology that target telomerase; ii) pharmaceuticals that activate
telomerase in tissues impacted by senescence, injury or degenerative
disease; and iii) cell-based therapies derived from its human
embryonic stem cell platform for applications in multiple chronic
diseases.

    This news release may contain forward-looking statements made
pursuant to the "safe harbor" provisions of the Private Securities
Litigation Reform Act of 1995. Investors are cautioned that such
forward-looking statements in this press release regarding future
financial results of Geron Corporation and potential applications of
Geron's technologies constitute forward-looking statements that
involve risks and uncertainties, including, without limitation, risks
inherent in the development and commercialization of potential
products, need for regulatory approvals or clearances, the maintenance
of our intellectual property rights and need for future capital.
Actual results may differ materially from the results anticipated in
these forward-looking statements. Additional information on potential
factors that could affect our results and other risks and
uncertainties are detailed from time to time in Geron's periodic
reports, including the annual report on Form 10-K for the year ended
December 31, 2004.


                           GERON CORPORATION
            CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                              (UNAUDITED)

                                                THREE MONTHS ENDED
                                                     MARCH 31,
(In thousands, except share and                  2005         2004
per share amounts)                           ------------ ------------

License fees and royalties                   $        59  $       248

Operating expenses:
  Research and development                         6,473        5,718
  Acquired in-process research technology             --       45,150
  General and administrative                       3,949        1,391
                                             ------------ ------------
 Total operating expenses                         10,422       52,259
                                             ------------ ------------
Loss from operations                             (10,363)     (52,011)

Interest and other income                            847          498
Interest and other expense                          (172)        (170)
                                             ------------ ------------
Net loss                                     $    (9,688) $   (51,683)
                                             ============ ============

Basic and diluted net loss per share         $     (0.18) $     (1.28)
                                             ============ ============
Weighted average shares used in calculation
   of basic and diluted net loss per share    54,175,184   40,449,815
                                             ============ ============


                 CONDENSED CONSOLIDATED BALANCE SHEETS

                                              MARCH 31,   DECEMBER 31,
(In thousands)                                  2005         2004
                                             ------------ ------------
                                             (Unaudited)    (Note 1)
Current assets:
  Cash, restricted cash and cash equivalents    $  8,060     $ 10,376
  Marketable securities                          116,955      110,118
  Interest and other receivables                   1,638        1,550
  Other current assets                             2,824        2,733
                                             ------------ ------------
Total current assets                             129,477      124,777

Property and equipment, net                        1,975        2,089
Deposits and other assets                          3,476        3,876
Intangible assets                                    942        1,131
                                             ------------ ------------
                                                $135,870     $131,873
                                             ============ ============

Current liabilities                                5,142        8,458
Noncurrent liabilities                               988        1,352
Stockholders' equity                             129,740      122,063
                                             ------------ ------------
                                                $135,870     $131,873
                                             ============ ============

Note 1: Derived from audited financial statements included in the
        Company's Annual Report on Form 10-K, filed with the SEC.

    CONTACT: Geron Corporation
             David L. Greenwood, 650-473-7765