Patients: For patients who do not already have a central venous catheter (plastic tube), one is placed into a major vein. This tube can stay in the body the entire treatment period for giving medications, transfusing blood, , withdrawing blood samples, and delivering the donated stem cells. Before the transplant procedure, patients receive from one to three cycles of "induction" chemotherapy, with each cycle consisting of 5 days of fludarabine, cyclophosphamide, etoposide, doxorubicin, vincristine, and prednisone followed by at least a 17-day rest period. All the drugs are infused through the catheter except prednisone, which is taken by mouth. After the induction therapy, the patient is admitted to the hospital for 5 days of chemotherapy with high doses of cyclophosphamide, melphalan, and fludarabine. Two days later, the stem cells are infused. The anticipated hospital stay is about 3 weeks, but may be longer if complications arise. Patients are discharged when their white cell count is near normal, they have no fever or infection, they can take sufficient food and fluids by mouth, and they have no signs of serious graft-versus-host disease (GVHD)-a condition in which the donor's cells "see" the patient's cells as foreign and mount an immune response against them.