Abstract: The invention features a method designed to lengthen the time an implanted organ (a xenograft) survives in a xenogeneic host prior to rejection. Preparation of the recipient for transplantation includes the following steps: First, the recipient is administered low dose radiation. Second, an antibody preparation that binds T cells and NK cells is injected into the recipient. Third, natural antibodies are absorbed from the recipient's blood by hemoperfusion of an organ of the donor species. Fourth, hematopoietic stromal tissue of the donor species is administered to the recipient. Fifth, donor hematopoietic stem cells are injected into the recipient. Finally, the xenograft organ is implanted into the recipient mammal. Best results are obtained when all steps are used in combination.