This paper develops a model of the cell cycle from the assumption that the rate of progression from one mitosis to the next is limited by the time taken to complete a defined sequence of rate-limiting chemical reactions. The model is shown to be related to earlier models which represent limiting forms of this more rigorous description. Earlier models were classified as stochastic or deterministic, but in this case, while the overall structure is deterministic, the individual steps are stochastically variable. Thus, this description demonstrates that both views were partially correct but were incomplete in detail. By applying the model to several experimental cell cycle curves, sets of coefficients corresponding to reaction rate constants could be obtained. A striking feature of these results is that only a small number (1-3) of slow steps dominated the rate of cell division. A discussion of some recent experimental results suggests possible candidates for the few slow rate-limiting steps, and outlines a rigorous method of testing the model.