AMENDED: To assess whether didanosine (ddI) will be better tolerated than AZT administered by either continuous intravenous delivery or oral administration (ddI arm removed per amended version).To determine whether ddI will achieve comparable clinical efficacy as the continuous intravenous route of delivery of AZT, and to assess whether either or both of these regimens are superior to that achieved with an intermittent AZT dosage schedule. To determine whether there are differences in patient or parent (guardian) compliance between the three treatment regimens. Original design: To determine whether the pharmacokinetic profile (bloodstream levels) of zidovudine (AZT) influences its effectiveness on HIV infection in children. That is, the study seeks to find out whether there is a difference in the effect of AZT when given as a continuous intravenous infusion (and, if available, an oral sustained release dose) compared to an intermittent (not continuous) dose given orally every 6 hours. The study also plans to determine (1) whether there are differences in the tolerance and side effects associated with AZT when given on an intermittent schedule as opposed to a steady-state schedule; (2) the extent of variation from patient to patient in AZT levels and whether the plasma and cerebrospinal fluid levels of AZT are related to the degree of therapeutic effectiveness; and (3) whether there are differences in the response of children who acquired HIV infection perinatally (just before, during, or just after the time of birth) versus those who acquired HIV infection by transfusion.