<qa>  What is the immune system that rejects the donors stem cells?RATIONALE: Giving chemotherapy and total body irradiation before a donor bone marrow transplant or peripheral blood stem cell transplant helps stop the growth of cancer cells. It also helps stop the patients immune system from rejecting the donors stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patients bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the bodys normal cells. Giving antithymocyte globulin and removing the T cells from the donor cells before transplant may stop this from happening. 