Total body irradiation combined with high dose cyclophosphamide followed by allogeneic bone marrow transplantation has proved to be a highly effective treatment for acute leukemia. However, a most troublesome complication was GVHD which occurred in a high proportion of patients. In spite of the application of immunosuppressive drugs after the transplantation, GVHD caused 25% mortality in these patients. Depletion of T lymphocytes from the donor bone marrow prior to grafting has proved to be highly effective in preventing GVHD. Experiments with monkeys and dogs demonstrated that engraftment of T cell depleted marrow requires an increase of the TBI dose for conditioning. Most clinical transplant teams that did not adjust their conditioning regimen reported a high incidence of graft rejections following the use of T cell depleted marrow, as well as an increased relapse rate. Transplant teams that increased their conditioning dose of TBI report an excellent take of T cell depleted marrow. On the basis of the relation between leukemia cell kill and probability of relapse, taking into account the radiosensitivity of leukemia cells, it can be calculated that the graft-versus-leukemia effect experienced with unmodified bone marrow grafts equals 1 log leukemic cell kill. This extra anti-leukemic effect is provided by the larger TBI dose employed to achieve full engraftment of T cell depleted marrow. However, increasing the immunosuppression by conditioning with anti-lymphocyte sera or TLI is not expected to prevent an increased relapse rate, since these conditioning modalities do not provide the necessary extra killing of leukemic cells.