OUTLINE: This is a dose escalation study. Phase I: Patients receive fludarabine IV over less than 30 minutes for 1-3 days. Treatment repeats every 4 weeks for up to 4 courses in the absence of relapse of underlying disease, malignancy, graft rejection, or unacceptable toxicity. Patients with progressive graft versus host disease after completion of 3 courses are taken off study. Patients with complete response are taken off study. Patients with partial response may continue treatment at the immediate prior dose level. Cohorts 3-6 patients receive escalating doses of fludarabine until the maximum tolerated dose (MTD) is determined. The MTD is defined as the dose preceding that at which 3 of 6 patients experience dose limiting toxicity. Phase II: Patients receive fludarabine at the MTD from phase I of the study.