OUTLINE: This is a randomized, multicenter study. Patients are stratified by center. Patients receive myeloablative therapy according to diagnosis: those with acute lymphocytic leukemia and lymphoblastic lymphoma are treated with total body irradiation (TBI), with a testicular and chest wall boost as appropriate, followed by cyclophosphamide (CTX); patients with undifferentiated or biphenotypic leukemia or with acute or chronic myelocytic leukemia are treated with CTX followed by TBI. Patients are then randomly assigned to receive non-T-cell-depleted, unrelated marrow versus T-cell-depleted, unrelated marrow. The modified marrow is depleted of T-lymphocytes by counterflow elutriation and positively selected for CD34 cells. Graft-versus-host disease (GVHD) prophylaxis with cyclosporine and methotrexate is given to the unmodified marrow group. Patients who receive modified marrow are given antithymocyte globulin (or methylprednisolone) for graft rejection prophylaxis before transplantation and cyclosporine and methylprednisolone for GVHD prophylaxis after transplantation.