The current optimal clinical management of HIV infection involves therapy with combinations of nucleoside and nonnucleoside reverse transcriptase inhibitors and HIV protease inhibitors. These regimens, though effective, do not completely eliminate HIV and the development of drug resistance is a major clinical problem. Interferons have been proposed as a possible treatment of HIV. Interferon-alfa inhibits HIV replication in vitro, and HIV-infected patients appear to have reduced production of interferons. Previous short-term clinical studies in adults showed anti-HIV activity, although there were safety and tolerability problems associated with the higher dose regimens used. This study will utilize a rising multiple-dose design to assess the safety, tolerability, and pharmacokinetics of single and multiple doses of PEG-Intron in HIV-infected children.