To evaluate the safety and toxicity of combination therapy for AIDS-associated Kaposi's sarcoma with zidovudine (AZT) and two kinds of interferon alpha. The two kinds are interferon alpha (IFN-A) and interferon alpha-2A (recombinant) (IFN-A2A). To define the pharmacokinetics of both AZT and IFN-A or IFN-A2A when given in combination; to define the maximum tolerated dose of each drug in combination and to define doses to be used in Phase II trials. AZT has been found to inhibit both the in vitro (in test tube) and cell killing effects of HIV, and both interferons (IFN-A and IFN-A2A) have shown antiviral and antitumor effect in Kaposi's sarcoma. It is reasonable to assume that a synergistic effect and enhanced antitumor response may be seen with combination therapy. A study to evaluate the safety and efficacy of AZT in combination with IFN-A or IFN-A2A is warranted.