OUTLINE: This is a randomized study. Patients are stratified according to disease (acute lymphocytic leukemia (ALL) vs acute myeloid leukemia (AML), and age (20 and under vs over 20). Patients are randomized to one of two treatment arms. Patients under age 5 are nonrandomly assigned to Arm I and those over age 55 are nonrandomly assigned to Arm II. Arm I: Patients receive total body radiotherapy on days -7 through -4 followed by cyclophosphamide IV on days -3 and -2. Patients undergo allogeneic bone marrow transplantation (ABMT) IV over 2-4 hours on day 0. Patients also receive standard graft vs host disease prophylaxis with cyclosporine and methotrexate. Arm II: Patients receive total body radiotherapy on days -9 through -6, thiotepa IV on days -5 and -4, and cyclophosphamide as in Arm I. Patients undergo T-cell depleted ABMT IV over 15 minutes on day 0. Patients over age 15 receiving bone marrow from female donors over age 30 or from male donors of any age also receive graft rejection prophylaxis consisting of antithymocyte globulin IV over 6-8 hours on days -5 and -4 and oral methylprednisolone twice daily on days -5 and -4. Beginning 2 months following transplantation, adult patients with AML and a prior history of CNS disease, all adult patients with ALL, and all pediatric patients (ALL and ANLL) receive CNS leukemia prophylaxis with cytarabine intrathecally with the diagnostic lumbar puncture and then monthly for 5 months (1 year in patients with a prior history of CNS leukemia).