As the shortage of available organs for transplantation becomes critical, many investigators have turned to the possibility of using animals as a source of donor organs. Although there have been several attempts to use organs from closely related species for transplantation into human, there is relatively little experience in the use of nonprimate animals as clinical donor animals. The major problem in transplants between widely disparate species is hyperacute rejection, a rapid and violent rejection reaction that leads to the destruction of the graft within minutes or hours. Hyperacute rejection appears to be triggered by components of natural immunity, most notably natural antibodies and complement. Recent data suggest that hyperacute rejection may not represent an insurmountable barrier to discordant xenotransplantation. There have recently been several examples of survival of grafts in recipients in the face of antigraft antibodies and an intact complement system referred to as accommodation. Once hyperacute rejection can be averted, it becomes necessary to consider elicited cellular responses. There are a number of issues to be considered in the clinically relevant model of porcine to primate xenografts. These include the size of the responding T-cell repertoire and the extent to which the cell adhesion molecules and cytokines of the donor will be able to stimulate recipient immune responses. Finally, the interactions between T cells and the cells forming the inner layer of blood vessels may have profound effects on the outcome of the graft.