It is estimated that approximately 75% to 80% of patients with AIDS experience anemia, which can be caused by AIDS or by the therapy patients receive for AIDS treatment (for example, zidovudine [AZT]). Anemia is a condition in which a patient has below normal levels of hemoglobin, the substance in red blood cells that carries oxygen to all parts of the body. People with severe anemia may experience fatigue and shortness of breath with activity. Therefore, this condition can have a negative influence on a person's quality of life. Epoetin alfa, used to treat anemia, is a genetically engineered form of a natural hormone, erythropoietin, that stimulates red blood cell production. This is a randomized, double-blind, placebo-controlled, parallel group study with an open-label follow-up period that is designed to evaluate the safety and effectiveness of epoetin alfa treatment in patients with AIDS who are being treated with AZT. The study consists of 3 periods: a screening period to determine if patients are eligible for the study, a double-blind treatment period, and an open-label treatment period. Eligible patients will be randomly assigned to one of two groups: epoetin alfa 150 units per kilogram or matching placebo. Patients will be treated with study medication (injected under the skin) 3 times a week for 12 weeks, or until their hematocrit reaches 38% to 40%. In the open-label period, all patients receive epoetin alfa injected under the skin for up to 6 months. Effectiveness will be determined by the change in hemoglobin and hematocrit (laboratory tests used to evaluate the severity of anemia), transfusion requirements, the patient's quality of life assessment, and the physician's global evaluation of the drug effect. Safety assessments include the incidence and severity of adverse events during the study, changes in clinical laboratory tests (hematology, biochemistry, and urinalysis), vital signs, electrocardiograms (ECGs), and physical examination findings. The study hypothesis is that AIDS patients who are receiving AZT and who are treated with epoetin alfa will have a lower incident of anemia compared with patients receiving placebo.