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 AZT and IFN-A or AZT and IFN-A2A when given in combination. To define the maximum tolerated dose (MTD) of each drug in combination and to define doses to be used in Phase II trial. AZT has been found to be effective against the effects of HIV in vitro (test tube) and both interferons have shown antiviral and antitumor effect on Kaposi's sarcoma. It is reasonable to assume that a synergism and an enhanced antitumor response may be seen with combination therapy. A study to evaluate the safety and effectiveness of AZT in the combination with IFN-A2A is warranted.