OUTLINE: This is a randomized, multicenter study. Patients will be stratified according to institution. Patients are assigned to one of two treatment arms, one with conventional bone marrow transplantation (arm I) and one with T cell depletion of the bone marrow (arm II). Arm I: Patients receive cyclophosphamide on days -6 and -5. Total body irradiation (TBI) is administered on days -4 to 0, although this order may be reversed. Males with ALL receive a testicular boost of radiation therapy. Bone marrow is infused on day 0. Patients receive cyclosporine beginning on day -1 and methotrexate IV on days 1, 3, 6, and 11. Arm II: T cell depletion is conducted by 2 different methods, according to the institution, and treatment varies depending on the method used. Method I is by T10B9 depletion and Method II is by counterflow elutriation depletion. Method I: Depending on the institution, some patients receive TBI on days -9 to -7 (before chemotherapy) (Course I) and some receive TBI on days -3 to -1 (after chemotherapy) (Course II). Course I also includes cytarabine IV on days -5 to -3, cyclophosphamide IV on days -2 and -1, and methylprednisolone IV on days -2 to 0 and 5-18. Bone marrow infusion is administered on day 0. Cyclosporine begins on day -1. Course II includes cytarabine IV on days -7 to -4 and cyclophosphamide on days -6 to -5. Methylprednisolone IV is administered on days -2 to 0 and 5-18. Bone marrow infusion is administered on day 0. Cyclosporine begins on day 0. Method II: Preparative therapy varies according to the disease category. Acute lymphoblastic leukemia: Patients undergo TBI on days -7 to -4. Males receive testicular boost on day -7, and all receive electron boost to anterior and posterior chest wall on days -5 and -4. Cyclophosphamide IV is administered on days -3 and -2. Bone marrow infusion is administered on day 0. Acute nonlymphocytic leukemia, chronic myelogenous leukemia, and myelodysplastic syndrome: Patients receive cyclophosphamide IV on days -7 and -6, followed by TBI on days -4 to -1. Bone marrow infusion is administered on day 0. Patients receive methylprednisolone IV every 12 hr on days -2,-1, and 5-19. Cyclosporine is administered from day -3 to day 180. All patients on both arms receive filgrastim (granulocyte colony-stimulating factor; G-CSF) beginning on day 7 post-transplant. Patients are followed weekly for the first 14 weeks, at day 100, every 6 months for 2 years, then annually thereafter.