Provided are methods for culturing and producing human cell containing compositions, such as organs and blood, in non-human mammal hosts and for the preparation of animal-hosted human cell containing compositions for transplantation to human subjects. In one aspect, non-human hosts genetically modified or treated to reduce the expression of xenoantigens, such as alpha-galactosyl epitopes, are used to reduce the transfer of xenoantigens to the hosted human cells. In another aspect, non-human hosts genetically modified to express or over-express molecules that promote immunological tolerance to a graft, such as hDAF, are used so that the molecules are transferred to the hosted human cells. These aspects facilitate the immunological acceptance of the human cell containing compositions upon transplantation to a human subject. Still another aspect provides conditioning treatments that facilitate the immunological acceptance of human cell containing compositions that have been supported in non-human hosts upon their transplantation to a human subject.