Exhibit 23.1 CONSENT OF INDEPENDENT ACCOUNTANTS We consent to the incorporation by reference in the registration statements of Genzyme Transgenics Corporation on Forms S-3 (File Nos. 33-82982, 33-97024, and 333-25769) and Forms S-8 (File Nos. 33-69516, 33-69518, 33-69520, 33-84706, 33-88030, 33-92970, 33- 92998, 333-04535, 333-29059, 333-29975, 333-29977, and 333-34119) of our report dated February 25, 1998, except as to the information presented in Note 13 for which the date is March 20, 1998, on our audits of the consolidated financial statements of Genzyme Transgenics Corporation as of December 28, 1997 and December 29, 1996 and for each of the three fiscal years in the period ended December 28, 1997, which report is included in this 1997 Annual Report on Form 10-K. /s/ COOPERS & LYBRAND L.L.P. COOPERS & LYBRAND L.L.P. Boston, Massachusetts March 27, 1998