[PALMER & DODGE LETTERHEAD]


                                                                     Exhibit 5.1

                                October 31, 2000



Genzyme Corporation
One Kendall Square
Cambridge, Massachusetts 02139

         We are rendering this opinion in connection with the Registration
Statement on Form S-4 (the "Registration Statement") filed by Genzyme
Corporation (the "Company"), a Massachusetts corporation, with the Securities
and Exchange Commission under the Securities Act of 1933, as amended (the
"Securities Act"), on or about the date hereof. The Registration Statement
relates to up to 8,677,672 shares (the "Merger Shares") of Genzyme General
Division Common Stock, $0.01 par value per share to be issued in connection
with the merger of GelTex Pharmaceuticals, Inc. ("GelTex") with and into
Titan Acquisition Corp. ("Merger Sub"), a wholly-owned subsidiary of the
Company, pursuant to the Agreement and Plan of Merger dated as of September
11, 2000, as amended by Amendment No. 1 dated as of October 19, 2000 (the
"Agreement") among the Company, GelTex and Merger Sub. We understand that the
Merger Shares are to be offered and sold in the manner described in the
Registration Statement.

         We have acted as your counsel in connection with the preparation of
the Registration Statement and are familiar with the proceedings taken by the
Company in connection with the authorization and issuance of the Merger
Shares. We have examined such documents as we consider necessary to enable us
to render this opinion.

         Based upon the foregoing, we are of the opinion that upon issuance in
accordance with the Agreement, the Merger Shares will be duly authorized,
validly issued, fully paid and nonassessable.

         The foregoing opinion is limited to the Massachusetts Business
Corporation Law and the federal laws of the United States.

         We hereby consent to the filing of this opinion as an exhibit to the
Registration Statement and to the reference to our firm under the caption "Legal
Matters" in the prospectus filed as part thereof.

                                               Very truly yours,

                                               /s/ Palmer & Dodge LLP

                                               PALMER & DODGE LLP