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Epidemiological analyses using the two-stage clonal expansion (TSCE) model indicate that low-dose radiation and exposure to some chemicals, such as arsenic or tobacco smoke, operate through several mechanisms during carcinogenesis. Typically, the most significant effect of these exposures is to increase the promotion of initiated cells. The estimated increases in promotion are small in absolute terms, yet highly significant, suggesting that initiated cells are almost, but not completely, under homeostatic regulation that serves to maintain the size of adult tissues and organs. To understand these effects better, we introduce a combined cell cycle and multistage carcinogenesis model with both deterministic and stochastic components. The model incorporates homeostatic regulation of cell cycle progression based on the difference between the total mean (deterministic) number and target number of stem cells. There are several reasons for extending carcinogenesis models to represent cell cycle states. First, the early mutations in many cancers appear to involve proteins associated with checkpoint control or other aspects of cell cycle regulation. Second, the sensitivity of cells exposed to radiation or chemicals changes markedly throughout the cell cycle. Modeling of damage and repair processes along with tissue homeostasis may be key to understanding the mechanisms that underlie promotion and other exposure-response phenomena. For example, loss of a checkpoint protein in initiated cells may shorten the cell cycle period and provide a slight growth advantage compared to normal cells in replacing cells damaged by endogenous processes, radiation, or chemical exposure.