Using this non-myeloablative allogeneic PBSCT approach, we will perform a Phase I study to evaluate the safety and feasibility of administering donor Th2 cells on day 1 post-transplant. Prior to transplantation, donor CD4+ T cells will be stimulated in vitro using culture conditions that support the generation of donor CD4 cells of the Th2 cytokine profile. If this Phase I study demonstrates that Th2 cell administration is safe and feasible, a Phase III study will be performed to evaluate whether Th2 cell administration reduces the incidence and severity of GVHD. Successful implementation of this Th2 strategy will greatly reduce the morbidity and mortality associated with allogeneic PBSCT, and may also represent an approach to stem cell transplantation in patients lacking an HLA-matched donor.