We fit a mathematical model to data characterizing the primary cellular immune response to lymphocytic choriomeningitis virus. The data enumerate the specific CD8+ T cell response to six MHC class I-restricted epitopes and the specific CD4+ T cell responses to two MHC class II-restricted epitopes. The peak of the response occurs around day 8 for CD8+ T cells and around day 9 for CD4+ T cells. By fitting a model to the data, we characterize the kinetic differences between CD4+ and CD8+ T cell responses and among the immunodominant and subdominant responses to the various epitopes. CD8+ T cell responses have faster kinetics in almost every aspect of the response. For CD8+ and CD4+ T cells, the doubling time during the initial expansion phase is 8 and 11 h, respectively. The half-life during the contraction phase following the peak of the response is 41 h and 3 days, respectively. CD4+ responses are even slower because their contraction phase appears to be biphasic, approaching a 35-day half-life 8 days after the peak of the response. The half-life during the memory phase is 500 days for the CD4+ T cell responses and appears to be lifelong for the six CD8+ T cell responses. Comparing the responses between the various epitopes, we find that immunodominant responses have an earlier and/or larger recruitment of precursors cells before the expansion phase and/or have a faster proliferation rate during the expansion phase.