A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. Key features are that the model is autonomous, except for dependence on external growth factors; variables are continuous in time, without instantaneous resets at phase boundaries; cell cycle controllers and completion of tasks associated with cell cycle progression are represented; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: Cyclin D1 in complex with Cdk4/6, APCCdh1, SCFβTrcp, Cdc25A, MPF, NUMA, securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors consistent with each main phase of the cell cycle. The response to growth factors shows restriction-point behavior. These results imply that the main features of the mammalian cell cycle can be accounted for in a quantitative mechanistic way based on known interactions among cycle control factors and their coupling to tasks involved in replication of DNA. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The most sensitive parameters are those associated with the initiation and completion of mitosis. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies.