Patients 15 years and older with moderately severe beta-thalassemia may be eligible for this study. Participants will take hydroxyurea daily at a dose calculated according to the patient's body size. Blood will be drawn weekly to measure blood cell and platelet counts. The drug dosage may be increased after 12 weeks of treatment and again after 24 weeks if the white cell and platelet counts remain stable. Patients who respond dramatically to treatment may continue to receive hydroxyurea for up to 3 years.