To evaluate and compare the long-term (48-177 weeks) safety, tolerance, and efficacy of two doses of zalcitabine ( dideoxycytidine; ddC ) taken orally every 8 hours in children with symptomatic HIV infection who have one of the following: intolerance to zidovudine ( AZT ) (development of toxicity during prolonged AZT therapy), demonstrated disease progression after 6 months of AZT therapy, OR both AZT intolerance and disease progression after 6 months of AZT therapy.