Patients will be assigned to 1 of 7 treatment groups. Both AZT and ddC will be given by mouth every 4 hours. One group will take AZT continuously for 52 weeks. One group will alternate 1 week of AZT with a week with no drug for 48 weeks and another group will alternate 1 week of ddC with a week of no drug for 48 weeks. Other groups will alternate AZT and either low-dose or high-dose ddC on a weekly basis or a monthly basis for 48 weeks. Patients will be seen weekly for the first 8 weeks of study and less often thereafter. Blood samples will be withdrawn frequently and evaluated for possible changes in the immune system, toxic effects, and possible changes in the amount of HIV in the blood. Lumbar punctures and skin biopsies will also be performed.