A nonhuman transgenic animal useful for providing organs, tissues, or cells for use in xenotransplantation, which is able to stably express (a) at least one transgenically encoded enzyme functional in said animal which masks or reduces the level of a zenoreactive antigen, said enzyme being a fucosyltransferase, and (b) at least one transgenically encoded complement inhibitor functional in humans, said animal being a source of transplant material, in the form of an organ, tissue, or cell, which is anatomically and physiologically compatible with a human recipient, wherein the likelihood or severity of hyperacute rejection of said material, as a result of transplantation of said material into a human patient, is reduced relative to the likelihood or severity of such rejection of said material in the absence of said expresssion, and wherein said animal is a pig.