OBJECTIVE To investigate the role of cellular repopulation in the dose-response relationship for radiation carcinogenesis resulting from high doses of radiation. METHODS A two-stage mathematical model of radiation carcinogenesis was developed and used to explore the effects of differing assumptions about repopulation by surviving normal stem cells and by one-stage mutants. RESULTS Characteristically, cancer incidence at any fixed time after irradiation increases with radiation dose, reaches a peak and then declines with dose (the decline reflecting radiation cell-killing). The optimal dose for cancer incidence, and the incidence level at this dose, are strongly influenced by repopulation kinetics. If repopulation does not occur, or is impaired owing to radiation damage to tissues, the highest value of cancer incidence is reduced, and this value occurs at a lower dose than if repopulation had been complete. A similar result is found if repopulation by one-stage mutants is impaired relative to unmutated cells, or if tissue recovery is assisted by immigration of unirradiated cells. CONCLUSIONS Differing repopulation kinetics can account for differing dose-response relationships after large doses of radiation. These findings are relevant to the occurrence of 'second tumours' following radiotherapy and to the interaction of radiation with other agents.