Lymphocytic choriomeningitis virus (LCMV) infection in mice provides an example of an extraordinarily dynamic process with an extreme sensitivity of phenotype of infection to parameters of virus/host interaction. A mathematical model is developed to examine the dynamics of virus-specific cytotoxic T lymphocyte (CTL) response for LCMV infection in mice. The model, formulated by a system of nonlinear delay-differential equations, considers the interacting populations of viruses, precursor CTLs, terminally differentiated effector CTLs and total virus antigen load. Clonal elimination of virus-specific cytotoxic T cells in high-dose LCMV-Docile infection represents an example of the classical phenomenon--high zone tolerance. To describe both conventional and exhaustive CTL responses in the acute phase of LCMV-D infection two mechanisms are invoked: the high virus antigen load inhibition of T-cells proliferation via energy induction and the activation-induced cell death by apoptosis. Parameters of the model, characterizing the rates of virus and CTL production and elimination in spleen, are estimated by assimilating with the model data on the LCMV-D infection in C57BL/6 mice for low-, moderate- and high-dose infections. It is suggested that not only the clonal expansions have to be described in mathematical models as being virus regulated but also the later phases of primary immune response. Down-regulation of the primary CTL response is controlled by a network of mechanisms inducing anergy and apoptosis in activated T cells. The model is used to investigate the effect of variations in virus and CTL response parameters on LCMV infection outcome and suggest predictions for experimental studies, in particular the phenotype of LCMV-WE infection in C57BL/6 as a function of initial virus doses.