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The dynamics of cell cycle and proliferating kinetics are characterized by the state equations, which are linear difference matrix equations with their state vectors consisting of variables representing cells in a particular compartment for cell-age, cell-size, and cell-DNA content. The transformation required from the cell-age distribution to the cell-size and DNA distributions in this discrete-time model under various assumptions is derived. The asymptotic behavior (as the time approaches infinity) of the cell age, cell size, and cell DNA is studied. The time course of the cell-size distribution of labeled cells under flash labeling is investigated by computer simulation and favorably evaluated with the experimental results obtained for spontaneous AKR leukemia-cell population.