Abstract
Generalisations of the two-mutation carcinogenesis model of Moolgavkar, Venzon and Knudson (to allow for an arbitrary number of mutational stages), and of the model of Armitage and Doll, are fitted to the Japanese atomic bomb survivor mortality data. Models with two or three mutations give adequate descriptions of the excess mortality of solid cancers. For leukaemia the fit of the three-mutation model is preferable to that of the two-mutation model. The optimal three-mutation leukaemia model provides a satisfactory fit only when both first and second mutation rates are radiation-affected. Examination of other epidemiological data leads to the conclusion that without some extra stochastic `stage' appended (such as might be provided by consideration of the process of development of a malignant clone from a single malignant cell) the two-mutation model is perhaps not well able to describe the pattern of excess risk for solid cancers that is often seen after exposure to radiation.
The optimal three-mutation models predict low-dose population risks for a current UK population of 
excess cancer deaths 
, 
radiation-induced cancer deaths or 1.0 - 1.4 years of life lost . Risks for a current Japanese population are 
excess cancer deaths , 
radiation-induced cancer deaths , or 1.2 years of life lost .