1
                                                                    Exhibit 23.1


               CONSENT OF ERNST & YOUNG LLP, INDEPENDENT AUDITORS


We consent to the incorporation by reference in the Registration Statements 
(Form S-3 Nos. 333-70355 and 333-51013 and Form S-8 Nos. 333-12487, 333-33635, 
333-33637, 333-71181) and the related prospectuses of Geron Corporation of our 
report dated February 12, 1999, with respect to the financial statements of 
Geron Corporation included in the Annual Report (Form 10-K) for the year ended 
December 31, 1998.

                                       /s/ ERNST & YOUNG LLP
                                       ---------------------------------

Palo Alto, California
March 12, 1999