This Phase I/II open-label, dose-escalating, randomized study is divided into 2 parts. Patients may participate in Part A and/or Part B. Part A (single dosing): 12 patients are sequentially assigned to receive 1 of 3 doses of T-20 given once on Day 0 by SC injection into the abdomen, deltoid area, or anterior aspect of the thigh and once on Day 1 by IV infusion. Provided safety criteria are met, patients who complete Part A, or new enrollees who did not participate in Part A, enroll in Part B. Doses for Part B are determined by pharmacokinetic data obtained in Part A. [AS PER AMENDMENT 4/20/00: Current data has now projected a pediatric dose. Each child will move to chronic dosing in Part B provided the child has no Grade 3 or higher toxicity to study drug through Day 7 in Part A.] Part B (multiple dosing): Patients are randomly assigned to 1 of 3 dose cohorts to receive 24 weeks [AS PER AMENDMENT 12/7/00: 48 weeks] of treatment (optional extension to 48 weeks [AS PER AMENDMENT 12/7/00: 96 weeks]) with bid SC injections of T-20. Cohort 1 receives the dose identified in Part A (Dose 1) as the lowest dose that is well tolerated and that achieves the target trough plasma concentration. Cohort 2 receives the next higher dose from Dose 1 (Dose 2). Cohort 3 receives either Dose 1 or Dose 2, depending on the tolerability and antiviral activity of each dose. [AS PER AMENDMENT 4/20/00: Cohort 1 receives 30 mg/m2 SC bid (Dose 1); Cohort 2 receives 60 mg/m2 SC bid (Dose 2); and Cohort 3 receives Dose 1 or 2 SC bid.] On Day 7 of T-20 dosing, children begin a new antiretroviral therapy regimen chosen by the site investigator based on study parameters. (Abacavir and amprenavir are not allowed for this regimen.) [AS PER AMENDMENT 1/6/00: Abacavir and amprenavir are now allowed.] The first injection will be given in the clinic and a parent/guardian will be trained to give successive injections. [AS PER AMENDMENT 4/20/00: The 2 doses given prior to obtaining trough levels on Days 1 and 7 must be directly observed by medical personnel.] Patients undergo clinical and laboratory evaluations to monitor viral load, HIV-related symptoms, and pharmacokinetics at time points throughout the study. Patients participating in Part A are evaluated at the clinic on Days 0, 1, and 7. Patients participating in Part B are evaluated at the clinic 6 times during the first 3 weeks and then every 4 weeks through Week 24. [AS PER AMENDMENT 12/7/00: Patients participating in Part B are evaluated at the clinic 6 times during the first 3 weeks, every 4 weeks through Week 24, and then every 8 weeks through Week 48.]