Abstract: A method of xenotransplanting organs, tissues, cells or non-viable components which reduces or prevents antibody-mediated rejections, including hyperacute rejection, is provided wherein transgenic animals are produced that express at least one enzyme which masks or reduces the level of the antigenic Gal.alpha.(1,3)Gal or gal epitope, and at least one complement inhibitor such as CD59, DAF and/or MCP. The transgenic animals which express both a gal epitope-reducing enzyme and a complement inhibitor will have masked or reduced levels of the gal epitope and will be much less likely to produce an antibody-mediated rejection following transplantation, and the expression of the complement inhibitor will also suppress complement activation and reduce even further a severe immune reaction following the transplantation of donor organs, tissue, cells or non-viable components from the transgenic animals so produced.