Strains of human immunodeficiency virus (HIV) differ greatly in their ability to replicate in T4 cells. Fast-replicating strains are observed during the early and late stages of HIV infection, while slow-replicating strains prevail during the intermediate, latent, stage. The prevalence of slow-replicating strains has been attributed to these strains' ability to escape the immune response. However, how these strains are able to avoid being eliminated by an immune response for several years has not been explained. Recent experiments indicate that HIV may be selectively transferred from infected macrophages to T4 cells specific for HIV antigens. Thus, HIV may preferentially infect those T4 cells necessary for generating a protective immune response. To determine the conditions under which an HIV-specific immune response can be blocked, we developed a mathematical model incorporating the process of viral transfer from infected macrophages to HIV-specific T4 cells along with the known processes of macrophage-T4 interaction, immune stimulation, and viral infection of T4 cells and macrophages. Our model shows that the mechanism of viral transfer to HIV-specific T4 cells can allow slow-replicating strains of HIV to escape immune response under conditions in which an immune response occurs against fast-replicating strains. The model also suggests that in addition to slow replication, the ability to reduce or block T-cell activation may be an important characteristic of escape mutants.