We examine simple mathematical models to investigate the circumstances under which the dynamics of cytotoxic T–lymphocyte (CTL) activation and differentiation may result in the loss of virus specific CD8+ cells, a process known as CTL exhaustion. We distinguish between two general classes of viruses: (i) viruses infecting cells that are not involved in the immune response; and (ii) viruses infecting antigen presenting cells (APCs) and helper cells. The models specify host and viral properties that lead to CTL exhaustion and indicate that this phenomenon is only likely to be observed with viruses infecting APCs and helper cells. Moreover, it is found that for such viruses, a high rate of replication and a low degree of cytopathogenicity promote the exhaustion of the CTL response. In addition, a high initial virus load and a low CD4+ cell count promote the occurrence of CTL exhaustion. These conclusions are discussed with reference to empirical data on lymphocytic choriomeningitis virus and on human immunodeficiency virus.