On the day of the transplant, patients will be given cyclosporin to prevent graft-versus-host-disease, a disease in which the donor cells react against the patient's cells. They may also be given lymphocytes after the transplant to boost the immune system and destroy leukemia cells. After 30, 60 and 100 days, bone marrow cells and circulating lymphocytes will be checked to see how many are of donor cell origin. If less than 100 percent are of donor origin, more lymphocytes will be transfused. Patients will have physical examinations and blood tests at least weekly for 3 months and then periodically for 5 years.