A mathematical model of the regulation of cell division is suggested. The model is based on the hypothesis that the process giving rhythm to cell division is located in the cell membrane: i.e., the process of free-radical oxidation of membrane lipids. Much depends on the physical state of the membrane. In the membrane, phase transitions take place because of the changes in lipid composition. These transitions differ in normal and tumor cells: in normal cells they are sharp and hysteretic owing to the presence of a framework (membrane skeleton) on the surface of the membrane, while in tumor cells the integrity of the surface is violated so that the transitions are smooth. This model makes it possible to explain differences in the regulation of normal and cancer cell proliferation. Within the limits of the model, such phenomena as density dependent inhibition of growth, reverse transformation, influence of cyclic AMP and ions of Ca2+ on the cell cycle, the actions of serum and of proteases on the cycle, and so on, are explained. A rational scheme for the appearance of the selective damage found in tumor cells is proposed.