OUTLINE: Allogeneic CD8+ CMV-specific, major histocompatibility complex class I-restricted cytotoxic T-lymphocyte (CTL) clones (CD8+ CMV-specific CTL clones) and CD4+ CMV-specific T-helper (Th)-cell clones are harvested and cultured in vitro at least 2 weeks before bone marrow or peripheral blood stem cell (PBSC) transplantation. Bone marrow or PBSC are infused on day 0. Patients receive the first infusion of CD8+ CMV-specific CTL clones beginning between days 28 and 45 posttransplantation, followed 8 days later by the second infusion, followed 2 days later by the first infusion of CD4+ CMV-specific Th-cell clones. Patients who receive prednisone posttransplantation or have deficient CD8+ CTL responses (i.e., less than 50% of the response measured in the immunocompetent bone marrow donor) after the second infusion of CD8+ CMV-specific CTL clones receive a third infusion of CD8+ CMV-specific CTL clones and a second infusion of CD4+ CMV-specific Th-cell clones before day 67.