The hyperacute rejection of pig organs by primates, including humans, results from antibody-mediated complement activation. Protection from complement injury still leads to delayed rejection, which results from other mechanisms that may also be dependent on the presence of antibody. Anti-pig antibodies are directed largely, if not entirely, against α-galactose (αGal) epitopes on pig vascular endothelium. Prevention of antibody-antigen binding is being attempted by methods that (1) alter antigen expression on the donor organ or (2) deplete the potential recipient of anti-αGal antibody. To date, most progress has been made in depleting antibody by extracorporeal immunoadsorption using immunoaffinity columns of synthetic αGal oligosaccharides. A pig organ transplanted into a recipient baboon depleted of antibody functions for several days-in contrast to minutes to hours in unmodified baboons. The return of antibody, however, results in rejection of the graft. Pharmacologic immunosuppressive agents are relatively ineffective for prolonged suppression of anti-αGal production. Total-body irradiation and splenectomy are proving more successful. Studies are continuing with the aim of achieving a state of B cell tolerance toward αGal epitopes.