OUTLINE: Prior to peripheral blood stem cell transplant, patients undergo preparative cytoreduction. Patients receive total body irradiation (TBI) beginning on day -5. Radiotherapy is administered in 9 doses over 3 days (3 doses per day for 3 days). Male patients with acute lymphocytic leukemia receive an additional dose of radiation to the testicles. Patients who are ineligible for TBI due to prior radiotherapy receive 2 doses of melphalan IV on day -3. All patients receive cyclophosphamide IV over 1 hour on days -2 and -1. Anti-thymocyte globulin is also administered IV over 6 hours on days -2 and -1. Approximately 24-36 hours after the last dose of cyclophosphamide, peripheral blood stem cells obtained from the HLA matched related donor are infused into the patient. Patients do not receive graft-versus-host disease prophylaxis after transplant; however, all other forms of supportive care are provided. Patients are followed for 1 year.