A mathematical model for the cell cycle is proposed that incorporates the known biochemical reactions involving both cyclin A and cyclin B, the interactions of these cyclins with cdc2 and cdk2, and the controlling effects of cdc25 and weel. The model also postulates the existence of an as yet unknown phosphatase involved in the formation of maturation promoting factor. The model produces solutions that agree qualitatively with a wide variety of experimentally observed cell-cycle behaviour. Conditions under which the model could explain the initial rapid divisions of embryonic cells and the transition to the slower somatic cell cycle are also discussed.