Four escalating doses of PEG IL-2 are studied. Patients are stratified by CD4 level. CD4 levels in Group A are 200 to 500 cells/mm3; in Group B - 1 to less than 200 cells/mm3. Further stratification is by p24 positive or negative, antiviral therapy for more or less than a year, and zidovudine (AZT) versus didanosine (ddI). The duration of PEG IL-2 treatment is a maximum of 28 weeks. This is an outpatient study; patients will be observed for four hours after the first dose of PEG IL-2 and for one hour after subsequent doses.