1) To determine whether it is possible to remove and culture (increase in number and activate) in the laboratory, CD8(+) lymphocytes (white blood cells) from HIV-infected patients receiving zidovudine (AZT); 2) To determine the toxicity of returning to the patients intravenously the expanded and activated autologous cells (given to the patient from whom they were taken), with and without giving the patients recombinant interleukin-2 ( aldesleukin; IL-2 ) at the same time; 3) To radiolabel (mark) the CD8(+) lymphocytes with Indium 111, and then scan the patients to determine the distribution of the CD8(+) lymphocytes in those who are and are not given IL-2 infusions; 4) To determine the toxicity of IL-2 given at the same time with autologous CD8(+) lymphocytes; 5) To measure changes in the immunology of the subjects following these treatments.