To assess the safety and efficacy of subcutaneously administered sargramostim ( granulocyte-macrophage colony-stimulating factor; GM-CSF ) in increasing and maintaining the neutrophil count in HIV-infected adults who have developed neutropenia as a result of receiving the antiretroviral agent, zidovudine ( AZT ). To assess the safety and efficacy of subcutaneously administered GM-CSF in increasing and maintaining the neutrophil count in HIV-infected adults with pre-existing neutropenia who are at high risk of developing hematologic intolerance while receiving the antiretroviral agent, AZT, for the first time. To assess the potential therapeutic benefit of concomitant GM-CSF and AZT on the natural history of HIV infection and associated infectious complications.