Abstract. The cell-division cycle and apoptosis are key cellular processes deregulated during carcinogenesis. Recent work of Aguda and Algar suggests a modular organization of regulatory molecular pathways linking the cellular processes of division and apoptosis. We carry out a detailed mathematical analysis of the Aguda-Algar model to unravel the dynamics implicit in the model structure. In addition, we further explore model parameters that control the bifurcations corresponding to the aforementioned cellular state transitions. We show that this simple model predicts interesting behavior, such as hysteretic oscillations and different conditions in which apoptosis is triggered.1. Introduction. It is now widely accepted among cancer researchers that the cell-division cycle and the cell-death program (called apoptosis) are key cellular processes deregulated during carcinogenesis. Enhanced cell proliferation can be due to increased cell cycling, inhibited apoptosis, or both. Recently, Aguda and Algar [1] reviewed and analyzed the regulatory molecular pathways linking the initiation of the cell cycle and apoptosis. These authors suggested a modular organization of the complex networks and presented a corresponding kinetic model for the cellular state transitions from quiescence (nondividing) to cell cycling, and eventually to apoptosis as the strength of extracellular signaling increases. This kinetic model, however, was not analyzed in detail in the original paper. Here, we extend the mathematical analysis to show that this simple model predicts other interesting behavior, such as hysteretic oscillations and different conditions in which apoptosis is triggered.The modular structure of the Aguda-Algar model is shown in Figure 1. The lines that end with " " indicate that one module inhibits the other, and the lines that end with "→" indicate that one module activates the other. The modules involved correspond to intracellular signaling, cell cycle, apoptosis, and a control node of transcription factors that stimulate the expression of cell cycle and apoptosis genes.