OUTLINE: Patients receive fludarabine IV over 30 minutes 5 days a week. Treatment repeats every 28 days for 4 courses in the absence of disease progression. Patients undergo clinical staging after completion of course 4 of fludarabine followed by 2 months of observation. Patients with stable or responding disease receive alemtuzumab subcutaneously 3 days a week for 6 weeks. Patients undergo clinical staging again after completion of 6 weeks of alemtuzumab followed by 2 more months of observation. Patients are followed every 3 months for 1 year and then every 6 months for 8 years.