Blood Transplantation for Patients With Hematologic Malignancies or Bone Marrow Failure States

* Patients with acute leukemia, lymphoma that failed to respond or relapsed after chemotherapy or CML beyond first chronic phase. * Patients with aplastic anemia or myelodysplasia which failed to respond to primary therapy are eligible. * Patients with low grade lymphoma or CLL will only be eligible if they failed two chemotherapy regimens and have stage IV disease. * Patients must be \<age 50 with a related haploidentical donor (phenotypically one, two or three HLA A, B and DR antigen mismatched) donor. * Patients should have adequate hepatic and renal function with a bilirubin of less than or equal to 1.5mg%, SGPT less than or equal to 3x the upper limits of normal, and creatine less than or equal to 1.5mg%. * Patients with serious intercurrent medical illness are not eligible. * Patients and their donors must provide written informed consent.