The study of the molecular mechanisms determining cellular programs of proliferation, differentiation, and apoptosis is currently attracting much attention. Recent studies have demonstrated that the system of cell-cycle control based on the transcriptional regulation of the expression of specific genes is responsible for the transition between programs. These groups of functionally connected genes form so-called gene networks characterized by numerous feedbacks and a complex behavioral dynamics. Computer simulation methods have been applied to studying the dynamics of gene networks regulating the cell cycle of vertebrates. The data on the regulation of the key genes obtained from the CYCLE-TRRD database have been used as a basis to construct gene networks of different degrees of complexity controlling the G1/S transition, one of the most important stages of the cell cycle. The behavior dynamics of the model constructed has been analyzed. Two qualitatively different functional modes of the system has been obtained. It has been shown that the transition between these modes depends on the duration of the proliferation signal. It has also been demonstrated that the additional feedback from factor E2F to genes c-fos and c-jun, which was predicted earlier based on the computer analysis of promoters, plays an important role in the transition of the cell to theS phase.