A new mathematical model of (\mathrm{T}) helper-cell activation and proliferation is investigated. The model incorporates recent data and theories about memory (T) cells. It accounts for the interacting population dynamics of resting, activated and memory (\mathrm{T}) helper cells, interleukin 2 and replicating antigen, and is able to mimic a broad range of available data on (\mathrm{T}) helper-cell proliferation and the effects of interleukin 2. The model is tested against existing in vitro data. It is then used to make novel interpretations of some recent experimental findings and predictions about the outcome of further experiments. Predictions made by the model fall into three groups concerning persistent infections, cell transfer experiments, and the return of memory cells to the resting state. The model predicts the existence of a group of persistent infections which result from slow growing replicating antigens and can be cleared by a boosting dose of antigen. A threshold is derived for the number of cells that must be transferred in order to transfer long-term immune memory from one animal to another. The existence of such a threshold implies that when small numbers of cells are transferred, or the transferred cells are in the resting state, cells alone cannot confer long-term memory on a recipient animal. However, if enough activated cells are transferred, it is possible to transfer long-term immune memory without antigen. The biological significance of a pathway whereby memory cells can lose their phenotypic and functional differences to return to the resting state is studied. A threshold concerning the rate of that return is derived; and it is only if the rate of return is above that threshold is there any impact on the response to a replicating antigen.