EXHIBIT 99.1

        Geron Corporation Reports 2004 First Quarter Financial
                               Results and Events


    MENLO PARK, Calif.--(BUSINESS WIRE)--April 29, 2004--Geron Corporation
(Nasdaq:GERN) today reported financial results for the three months ended March
31, 2004.
    For the first quarter of 2004, the company reported operating revenue of
$248,000 and operating expenses of $52.3 million compared to $262,000 and $8.3
million, respectively, for the comparable period in 2003. Net loss for the
period was $51.7 million or $(1.28) per share compared to $7.9 million or
$(0.32) per share for the comparable period in 2003.
    The increase in first quarter 2004 operating expenses was attributable to a
non-cash charge of $45.2 million to acquire in-process research technology,
which resulted from the licensing of technology rights from Merix Bioscience,
Inc. Excluding that charge, the company's overall operating expenses decreased
in the first quarter of 2004 as a result of lower personnel-related costs and
lower costs for raw materials to manufacture clinical trial drugs.
    In connection with the Merix transaction, Geron issued five million shares
of its common stock to Merix in exchange for a co-exclusive right under patents
controlled by Merix for the use of defined antigens in therapeutic cancer
vaccines. The dendritic cell technology covered by the Merix patents is
currently being used in conjunction with Geron's proprietary telomerase
technology in a Phase I/II clinical trial underway at Duke University Medical
Center. The addition of the Merix license to Geron's telomerase rights broadens
the company's proprietary position in the technology being tested in this trial,
and will serve as the foundation for Geron's work towards developing
telomerase-based cancer vaccines. Geron maintains exclusive rights to the use of
telomerase in these vaccines through its own patent estate. Except for payments
that flow through to third party academic licensors from whom Merix originally
obtained its rights, the license acquired by Geron is fully paid up.
    The company expects its research and development expenses to increase in the
future as it continues pre-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 2004 and 2003 represented reimbursement
for consulting agreements with various biotechnology companies, 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 promoter
technology.

    First Quarter 2004 Highlights:

    --  The Board of Patent Appeals and Interferences of the U.S. Patent and
        Trademark Office issued a decision on motions filed in the patent
        interference proceeding between Geron and Infigen, Inc. of DeForest,
        Wisconsin relating to nuclear transfer technology. The decision upholds
        the patentability of all of Geron's claims and finds all of the Infigen
        claims to be unpatentable.

    --  The Board of Patent Appeals and Interferences of the U.S. Patent and
        Trademark Office issued a final judgment ending the patent interference
        proceeding between Geron and Infigen, Inc. of DeForest, Wisconsin. The
        Board awarded judgment in Geron's favor on all counts in the
        interference.

    --  Geron acquired certain rights from Merix, as described more fully above.

    --  The Board of Patent Appeals and Interferences of the U.S. Patent and
        Trademark Office issued a decision on motions filed in the patent
        interference proceeding between Geron and Advanced Cell Technology
        Corporation of Worcester, Mass., relating to nuclear transfer
        technology. The decision finds all claims in the issued ACT nuclear
        transfer patent to be unpatentable. All motions filed by ACT were
        denied, including motions attacking the patentability of Geron's claims.

    --  Geron granted to Xcellsyz a nonexclusive license to Geron's human
        telomerase reverse transcriptase (hTERT) technology for research
        applications and the development of research products.

    --  Several presentations were made at the American Association for Cancer
        Research (AACR) Annual Meeting in Orlando, Florida of additional data
        from preclinical studies of GRN163L, a potent and specific telomerase
        inhibitor. The results presented confirm and extend the in vitro and in
        vivo efficacy of GRN163L in solid tumors, specifically liver and ovarian
        cancer, and report a sensitive, accurate, and reproducible assay for the
        detection of the drug in human blood.

    Geron is a biopharmaceutical company focused on developing and
commercializing therapeutic and diagnostic products for cancer based on its
telomerase technology, and cell-based therapeutics using its human embryonic
stem cell technology.

    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 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 quarterly report on Form 10-Q for the quarter ended March 31,
2004.

    Additional information about the company can be obtained at
http://www.geron.com.


                                GERON CORPORATION
                 CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

                                               THREE MONTHS ENDED
                                                    MARCH 31,
(In thousands, except share and                2004          2003
per share amounts)                             ----          ----


Revenues from collaborative agreements     $         --  $         36
License fees and royalties                          248           226
                                           ------------- -------------
   Total revenues                                   248           262

Operating expenses:
  Research and development                        5,718         6,850
  Acquired in-process research technology        45,150            --
  General and administrative                      1,391         1,456
                                           ------------- -------------
   Total operating expenses                      52,259         8,306
                                           ------------- -------------
Loss from operations                            (52,011)       (8,044)

Interest and other income                           498           276
Interest and other expense                         (170)         (164)
                                           ------------- -------------
Net loss                                   $    (51,683) $     (7,932)
                                           ============= =============

Basic and diluted net loss per share       $      (1.28) $      (0.32)
                                           ============= =============
Weighted average shares used in calculation
 of basic and diluted net loss per share     40,449,815    24,935,574
                                           ============= =============


                 CONDENSED CONSOLIDATED BALANCE SHEETS


                                               MARCH 31,     DEC 31,
(In thousands)                                   2004         2003
                                                 ----         ----
                                             (Unaudited)    (Note 1)
Current assets:
  Cash, restricted cash and cash equivalents  $    7,059   $   13,353
  Marketable securities                           92,673       96,427
  Interest and other receivables                   5,477        1,146
  Other current assets                             4,157          882
                                             ------------ ------------
Total current assets                             109,366      111,808

Property and equipment, net                        1,558        1,684
Deposits and other assets                            648          804
Intangible assets                                  3,103        3,819
                                             ------------ ------------
                                              $  114,675   $  118,115
                                             ============ ============

Current liabilities                                7,040        9,825
Noncurrent liabilities                             1,181        1,966
Stockholders' equity                             106,454      106,324
                                             ------------ ------------
                                              $  114,675   $  118,115
                                             ============ ============

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