Several dideoxynucleosides have now been shown to have activity against HIV but to have different toxicities. This study will involve therapy of patients with AIDS or ARC with two of these agents, AZT and 2', 3'-dideoxyinosine (ddI), which have different toxicity profiles, over a 2-year period of time. The rationale for using the two drugs will be to reduce toxicity and also possibly to delay or prevent the development of resistance. Patients will be randomized to receive either an alternating regimen or a continuous simultaneous regimen with these two drugs. The study will be structured as a randomized pilot study.