A new function is proposed for describing the rate of T cell proliferation in response to peptides on antigen-presenting cells. The model improves an earlier model of ours by allowing for a true maximum proliferation rate of the T cells. This is achieved by a simple change of variables that markedly relaxes the conditions for a conventional quasi-steady-state assumption. The new model has the same "ecological" properties as the previous one. Thus the natural competition in the model allows for regulation of T cell population size in the presence of continuous stimulation by antigen. An important feature is the competitive exclusion of T cell clones recognizing the same peptide with different affinities allowing for "affinity selection". Models for the population dynamics of experienced, naïve and activated T cells are also developed. These T cell subpopulations compete with one another for antigen. In models with lymphokine production a "proliferation threshold" is obtained that allows for tolerance.