In Stage 1 of the study, a minimum of 22 patients are randomized to each of three treatment arms: didanosine (ddI) plus AZT plus nevirapine (NVP); ddI plus AZT; and ddI plus NVP. After 12 weeks of treatment, the study proceeds to Stage 2 provided at least 40 percent of patients in Stage 1 show a reduction of at least 40 percent from baseline ICD p24 antigen of greater than or equal to 70 pg/ml AND fewer than two patients experience grade 4 rash. Patients in Stage 1 continue treatment for an additional 36 weeks. In Stage 2, additional patients are randomized to each original treatment regimen until a maximum of 130 patients per arm have been entered. Stage 2 patients receive treatment for at least 48 weeks.