a change in the host donor specific antibody response or by a change in the host lymphocyte response to donor antigen as is needed to maintain or otherwise prolong the acceptance of a graft thus method of the invention can be modified to include a further step of determining if a subject is in need of cytokine therapy and if so administering a cytokine the period over which the cytokine s is administered or the period over which clinically effective levels are maintained in the subject can be long term e g for six months of more or a year or more or short term e g for a year or less more preferably six months or less more preferably one month or less and more preferably two weeks or less the period will generally be at least about one week and preferably at least about two weeks in duration in preferred embodiments the recipient is a primate e g a human and the donor is from a different species e g the donor is a pig and pig scf is administered pig il 3 is administered a combination of pig scf and pig il 3 is administered a pig specific hematopoiesis enhancing factor e g pig gm scf is administered e g after the implantation of a graft e g about a month after the implantation of a graft a particularly preferred embodiment combines a short course e g about a month of cyclosporine or a similar agent a short course e g about two weeks of 15 deoxyspergualin or a similar agent and a short course e g about two weeks of donor specific cytokines e g scf and il 3 it is to be understood that while the.