Exhibit 99.1

    Transgenomic Inc. Continues to Provide Specialty Nucleic Acid Products to
                                Geron Corporation

     Ongoing Support for Manufacture of Geron's Novel Cancer Therapeutic

    OMAHA, Neb., April 28 /PRNewswire-FirstCall/ -- Transgenomic Inc.
(Nasdaq: TBIO) announced today it has agreed to provide additional quantities
of modified nucleic acid building block compounds to Geron Corporation
(Nasdaq: GERN) under terms of multiple new addendums to an existing Master
Supply Agreement between the two companies. The compounds will be used in the
synthesis of Geron's anti-cancer drug GRN163L.  GRN163L is a
thio-phosphoramidate oligonucleotide, a new class of synthetic nucleic acid
that has a number of potential advantages over earlier-generation synthetic
nucleic acid chemistries, including enhanced sequence-specific DNA and RNA
binding activity, high resistance to degradation, and improved uptake and
biodistribution properties.  Product shipments under the new addendums
commenced in the first quarter of 2004 and are expected to extend into the
third quarter.
    "We are pleased to have the opportunity to provide ongoing manufacturing
support to Geron as they continue to develop their novel cancer therapeutics,"
said Collin D'Silva, Transgenomic's CEO.  "We are well positioned to provide
process development and manufacturing support for cutting-edge nucleic acid
chemistries, such as the phosphoramidate-based chemistry upon which their lead
molecules are based."  D'Silva concluded, "We continue to sharpen our nucleic
acid building block manufacturing operation's focus on supporting the
manufacture of innovative, next-generation synthetic nucleic acids, a market
segment in which we have a significant competitive edge."

    About Transgenomic
    Transgenomic provides versatile and innovative research tools and related
consumable products to the life sciences industry for the synthesis,
separation, analysis and purification of nucleic acids and a wide variety of
nucleic acid-based specialty chemicals.  Transgenomic's BioSystems segment
offers its WAVE Systems(R) and associated consumables.  These systems are
specifically designed for use in genetic variation detection and single- and
double-strand DNA/RNA analysis and purification.  These systems have broad
applicability to genetic research and molecular diagnostics.  To date there
have been over one thousand systems installed in over 30 countries around the
world.  In addition, the BioSystems segment offers WAVE-based biomarker
discovery and validation services in support of translational research,
pre-clinical and clinical studies.
    Through its nucleic acids business segment, Transgenomic provides
specialty chemicals, including advanced nucleic acid building blocks and
associated reagents, used in applications such as genetic diagnostics and
therapeutics, as well as a comprehensive menu of services, including nucleic
acid chemistry R&D, process development, analytical methods development, cGMP
oligonucleotide manufacturing, quality control and regulatory support.
    For more information about the innovative genomics research tools
developed and marketed by Transgenomic, please visit the company's Web site at
www.transgenomic.com.

    Cautionary Statement
    Certain statements in this press release constitute "forward-looking
statements" of Transgenomic within the meaning of the Private Securities
Litigation Reform Act of 1995, which involve known and unknown risks,
uncertainties and other factors that may cause our actual results to be
materially different from any future results, performance or achievements
expressed or implied by such statements. Forward-looking statements include,
but are not limited to, those with respect to support of the manufacture of
innovative, next-generation synthetic nucleic acids.  The known risks,
uncertainties and other factors affecting these forward-looking statements are
described from time to time in Transgenomic's reports to the Securities and
Exchange Commission.  Any change in such factors, risks and uncertainties may
cause the actual results, events and performance to differ materially from
those referred to in such statements.  Accordingly, the company claims the
protection of the safe harbor for forward-looking statements contained in the
Private Securities Litigation Reform Act of 1995 with respect to all
statements contained in this press release.  All information in this press
release is as of the date of the release and Transgenomic does not undertake
any duty to update this information, including any forward-looking statements,
unless required by law.

SOURCE  Transgenomic Inc.
    -0-                             04/28/2004
    /CONTACT:  Mitchell L. Murphy, +1-402-452-5418, mmurphy@transgenomic.com,
or Robert J. Pogulis, Ph.D., +1-845-782-9617, rpogulis@transgenomic.com, both
of Transgenomic/
    /Web site:  http://www.transgenomic.com /
    (TBIO GERN)

CO:  Transgenomic Inc.; Geron Corporation
ST:  Nebraska
IN:  HEA MTC BIO
SU:  PDT