1. Any patient with hematologic or oncologic diagnosis in which allogeneic HSCT is thought to be beneficial, and in whom front-line therapy has already been applied. Patients treated on this protocol will be without morphological evidence of disease (complete remission or "CR"), or if the patient has evidence of disease, the patient must have had at least a good partial response (PR) to the most recent therapy and the disease must be chemoresponsive.