OBJECTIVES: I. Demonstrate that the graft versus host disease (GVHD) prophylactic regimen consisting of T-cell depletion and cyclosporine results in less toxicity than the control regimen of methotrexate and cyclosporine in recipients of peripheral blood stem cell transplants. II. Monitor safety of the two regimens in order to assure that the treatment regimen dose not result in any increase in serious or unexpected toxicities, does not compromise the efficacy of GVHD prophylaxis, and does not compromise the efficacy of the disease therapy.

OUTLINE: This is a multicenter, controlled, randomized trial. Patients are assigned to high or low risk groups and randomized to the control or treatment arms. Patients are stratified by risk group and by site. Mobilization, apheresis, and successful cryopreservation of the minimum number of CD34 cells for transplant has to be achieved prior to initiating cytoreductive therapy. Following intensive cytoreductive therapy, patients receive either unselected peripheral blood stem cells (PBSC) together with the control graft versus host disease (GVHD) prophylaxis regimen or CD34+ cells isolated from PBSC with cyclosporine. In the control group, GVHD prophylaxis consists of two drug therapies, cyclosporine and methotrexate. The cyclosporine is administered first by IV continuous infusion and then later orally, twice a day, in decreasing increments for 180 days. Methotrexate is administered by IV on days 1, 3, 6, and 11. Cyclosporine is discontinued after day +180 if there is no evidence of GVHD. In the treatment group, GVHD prophylaxis consists of T cell depletion of the transplant product using the Isolex positive selection procedure (Isolex selected CD34+ cells) and cyclosporine. The cyclosporine is administered at the same doses and increments as in the control group. In cases where there still is acute or chronic GVHD, the patient is given the appropriate salvage regimens. Patients are followed monthly for 6 months after transplant, and then for 2 years to monitor relapses.

PROJECTED ACCRUAL: There will be 200 patients accrued (100 in each arm) in this study.

DISEASE CHARACTERISTICS: - Acute lymphocytic leukemia (ALL) with documented chemosensitivity (complete response [CR], partial response [PR], or minor response [MR]) in first or second remission, first or second relapse, or high risk ALL with Ph positive 9/22 translocation; OR - Acute myelogenous leukemia (AML) with documented chemosensitivity (CR, PR, or MR) in first or second remission, or first or second relapse; OR - Chronic myelogenous leukemia (CML), chronic or accelerated, that is not in blast crisis; OR - Hodgkin's disease or non-Hodgkin's lymphoma with documented chemosensitivity in first or second relapse Consenting HLA-identical related donor required No active CNS or skin leukemia involvement No disease that requires additional mediastinal radiation

PATIENT CHARACTERISTICS: Age: 18-55 Performance status: Karnofsky 70-100% Life expectancy: Greater than 8 weeks Hematopoietic: Not specified Hepatic: Bilirubin less than 1.5 times normal SGOT less than 2 times normal Renal: Creatinine less than 1.5 times normal Cardiovascular: Left ventricular ejection fraction at rest at least 40% or within normal range Pulmonary: DLCO greater than 45% of predicted or within normal range Other: HIV negative At least 2 weeks since any active infection requiring intravenous treatment with antifungal, antibacterial or antiviral agents with the exception of coagulase negative staphylococcal line infection No coexisting medical problems that would significantly increase the risk of the transplant procedure Not pregnant or nursing

PRIOR CONCURRENT THERAPY: No more that 2 prior therapy regimens Biologic therapy: No prior autologous or allogeneic bone marrow or peripheral blood stem cell transplant Chemotherapy: Not specified Endocrine therapy: Not specified Radiotherapy: Prior radiation therapy subject to dose requirements Surgery: Not specified Other: At least 2 weeks since intravenous treatment with antifungal, antibacterial or antiviral agents, except for treatment of coagulase negative staphylococcal infection of an IV or central line