Children who show AZT intolerance and/or progressive disease after 6 months of AZT therapy receive oral ddI at 1 of 2 doses for a minimum of 48 weeks, with a 48-week extension. Patients are seen for clinical and laboratory evaluations at scheduled times during the study. (Per 5/12/92 amendment, new patients will not be enrolled in the pharmacokinetics studies.) Per 10/31/94 amendment: Patients are eligible to receive blinded study drug for an additional 8-16 weeks after the final on-study visit, but no later than 2/15/95.