A two-stage stochastic model for carcinogenesis was used to analyze the incidence of cancer of the lung, stomach and colon in the cohort of atomic bomb survivors. We fitted the model assuming that acute exposure to radiation results in the creation of initiated cells that are added to the pool of spontaneously initiated cells. In the cancers analyzed, with the exception of lung cancer in females, we found no evidence that radiation-induced initiation was dependent upon age at exposure. In contrast, we found that spontaneous initiation was dependent upon age at exposure in the cancers analyzed except stomach cancer among males. Because exposure to radiation in this cohort occurred at the same time for all members of the cohort, age at exposure is exactly correlated with birth cohort, and the dependence of spontaneous initiation on age at exposure is a reflection of the cohort effects seen in these cancers in Japan. Even without a dependence of radiation-induced initiation on age at exposure, the two-stage model can explain the temporal behavior of the excess relative risk with age at exposure and time since exposure. In particular, the model predicts that excess relative risk is highest among those exposed as children. Moreover, since radiation-induced initiation is not higher among those exposed as children, the excess relative risk in this group is not due to an inherently higher sensitivity to radiation. Our biologically based approach provides another perspective on the temporal behavior of risk after acute exposure to ionizing radiation.