One treatment modality that ameliorates or prevents GvHD following allogeneic marrow transplantation is T cell-depletion of donor marrow before infusion into the recipient. T cell-depletion can be divided into physical methods such as separation by elutriation or sheep cell rosetting, and immunologic methods which use a T cell-specific antibody(ies) plus complement or toxin to kill the cells. These different techniques may remove a subpopulation of T cells, all T cells, or T cells plus other cell types such as B cells or natural killer (NK) cells. The number of stem cells transferred may also be affected.