The study is being conducted in three stages. In Cohort A (IFN-A alone), four patients receive IFN-A; subsequent four-patient cohorts receive doses escalated in increments. If 50 percent or more of patients at any dose level experience grade 2 or better toxicity, doses in subsequent cohorts are escalated. If grade 3 or 4 toxicity is seen in one patient at a given dose level, two additional patients are enrolled at that level. Treatment is given subcutaneously (under the skin, with a needle), 3 times per week for 12 weeks. The MTD is defined as the dose level immediately below that at which 50 percent or more of patients experience grade 3 or 4 toxicity. In Cohort B (combination IFN-A plus AZT), patients who complete treatment in Cohort A continue on the same dose of IFN-A, and a low, middle, or high dose of AZT is added. In Cohort C, four newly assigned patients who have been on a stable prescribed dose of AZT of at least 90 mg/m2 for 6 weeks are treated at each of the same dose combinations as those in Cohort B. Treatment is given for 12 weeks. IFN-A is given subcutaneously 3 times a week and AZT is given orally every 6 hours. Dose levels of both drugs are increased until 50 percent or more of patients experience grade 3 or 4 toxicity in any dose level.