Patients with leukemia in clinical remission, and patients with refractory lymphoid malignancy will be candidates for this HLA-matched allogeneic PBSCT protocol. Patients will receive novel induction regimen (fludarabine and EPOCH) and transplant preparative regimen (fludarabine and cytoxan) designed to maximally deplete host immune T cells capable of mediating graft rejection. After induction and preparative regimen chemotherapy, patients will receive an unmanipulated, G-CSF mobilized PBSC graft. In the initial six patients receiving this transplant procedure at the NCI, graft rejection has been successfully prevented (100% donor chimerism by day 30 post-transplant). Importantly, GVHD has been observed in all six patients, with three of the six patients developing severe GVHD (grade III). Given that this regimen successfully achieves donor engraftment, and is associated with significant GVHD, this transplant regimen represents an excellent clinical setting for the evaluation of Th2 cells.