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 study with an open-label follow-up period that is designed to evaluate the safety and effectiveness of epoetin alfa treatment compared with placebo treatment in patients with AIDS who are being treated with AZT. The study consists of three periods: a screening period to determine if patients are eligible for the study, a double-blind period, and an open-label period. During the double-blind period, patients are randomly assigned to one of two groups and receive either epoetin alfa (100 units per kilogram) or placebo injected into a vein (intravenously) three times per 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 (subcutaneously) for up to 6 months at the dose needed to maintain hematocrit levels of 38% to 40%. Effectiveness will be determined by the change in hemoglobin, hematocrit, and reticulocyte count (laboratory tests used to evaluate the severity of anemia), transfusion requirements, and the patient's quality of life assessment. Safety assessments include the incidence and severity of adverse events during the study, results of clinical laboratory tests (hematology, biochemistry, and urinalysis), measurements of vital signs, electrocardiograms (ECGs) and physical examination findings. The study hypothesis is that for treatment of anemia in patients with AIDS who are receiving AZT therapy, epoetin alfa is superior to placebo, as measured by changes in hemoglobin, hematocrit, and reticulocyte count, transfusion requirements, and the patient's quality of life.