DISEASE CHARACTERISTICS: Hematologic malignancies of the following types: Chronic myelogenous leukemia (CML) in chronic or accelerated phase Newly diagnosed acute leukemia at high risk of relapse following chemotherapy alone Early referral encouraged so that donor search can begin as soon as possible Acute leukemia failing one cycle of induction chemotherapy Acute leukemia beyond first remission High-risk Hodgkin's disease and non-Hodgkin's lymphoma in first remission Hodgkin's disease, non-Hodgkin's lymphoma, or other malignant lymphoproliferative disease after first remission No suitable related donor available (i.e., no HLA genotypically identical sibling) No haploidentical relative with no more than 1 unshared haplotype for an HLA-A, -B, or -D locus Acute leukemia in relapse and CML in blast crisis eligible only under the following conditions: Patient's clinical condition is likely to remain stable for the 2-6 month period necessary to find a marrow donor Remission induction has been attempted Local physician and patient accept that the search or transplant may be canceled if the patient's condition deteriorates during the search No leukoencephalopathy Donor requirements: Age less than 60 In good health Phenotypically identical for HLA-A, -B, and -DRB1 1-antigen mismatch for HLA-A, -B, or -DRB1 locus allowed for patients below age 36 Patients for whom TBI is contraindicated may be treated on protocol FHCRC-739 Severe aplastic anemia should be transplanted according to protocols FHCRC-174.2 or FHCRC-800 Myelodysplastic syndrome should be transplanted according to protocol FHCRC-179.3 or FHCRC-844

PATIENT CHARACTERISTICS: Age: Under 56 Performance status: Not specified Life expectancy: Not specified Hematopoietic: Not specified Hepatic: No acute hepatitis No other severe hepatic disease Renal: Creatinine less than 2 times normal for age, weight, and sex Cardiovascular: No symptomatic cardiac disease Pulmonary: No active pulmonary disease No history of pulmonary fibrosis No severe hypoxemia (pO2 less than 70 mm Hg and DLCO less than 70%) No mild hypoxemia (pO2 less than 80 mm Hg and DLCO less than 60%) Other: HIV negative No severe limitations due to diseases other than malignancy

PRIOR CONCURRENT THERAPY: No more than 3,000 cGy to the whole brain No more than 1,500 cGy to the chest or abdomen At least 6 months since involved-field irradiation to the chest or abdomen