OBJECTIVES: I. Determine whether donor hematopoiesis can be safely established using a nonmyeloablative conditioning regimen followed by HLA matched sibling donor peripheral blood stem cell transplantation in patients with hematologic malignancies. II. Determine whether mixed chimerism can be safely converted to full donor hematopoiesis with this treatment regimen in these patients. III. Determine the toxicity and incidence of aplasia and graft versus host disease in these patients treated with this regimen. IV. Determine the antitumor potential of this treatment regimen in these patients. V. Determine the role of NFkB in the modulation of the cytokine secretion profile of T lymphocytes during an alloimmune response in these patients treated with this regimen.