Up to 90 patients are randomized to receive either low or high doses of IFN-alpha (1 or 10 million Units/day) in combination with a fixed dose of ddI. Fourteen patients are initially entered at each dose level. If no objective antitumor responses are observed among the first 14 patients at a given dose, no further patients are entered on that treatment arm. If one or more antitumor responses are seen at a given dose, up to 45 patients may be entered on that treatment arm. Patients must complete at least 4 weeks of study therapy to be considered evaluable for tumor response. Treatment is continued until tumor progression or unacceptable toxicity occurs. PER AMENDMENT 9/19/96: NOTE - After 16 weeks of treatment subjects may receive any FDA approved antiretroviral drug regimen in addition to or in place of ddI.