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