The incidences of some childhood cancers have been shown to fit a two-mutation hypothesis for cancer initiation. According to this hypothesis, the first mutation can be either germinal or somatic while the second is always somatic. A probabilistic model involving the mean number of tumors per genetically susceptible individual is developed as a function of age and is compared with age incidence data for retinoblastoma. The change in the mean number of tumors with time is interpreted in terms of the growth of retinal cells. In patients who are not genetically susceptible, the times of occurrence of the first and second somatic mutations can be inferred from a comparison of familial and non-familial unilateral case incidences. The total incidences of hereditary and nonhereditary forms of retinoblastoma are related to germinal and somatic mutation rates. The even distribution of certain childhood cancers throughout the world suggests that their incidences are determined by spontaneous mutation rates rather than by local environmental mutagenic carcinogens.