Models for the dose and age dependence of radiation induced cancer have been based primarily on the follow-up of the atomic bomb survivors. Two different concepts have been deduced for leukaemias and for other cancers. The excess leukaemias appear in a distinct temporal wave with a maximum 5 to 10 years after radiation exposure; the distribution is more narrow for younger ages, but there is little dependence of the total attributable risk on age at exposure. For other cancers the latent periods are longer and, according to the current interpretation, the excess rates are then proportional to the age specific spontaneous rates, so that most excess cases would arise at old age. The factors of proportionality, and thus the attributable risks, are assumed to be markedly higher for young ages at exposure. It is argued here that there is no firm support for this interpretation. The present analysis compares the current model for cancers other than leukaemia to a more meaningful alternative than the so-called additive model which is usually invoked as a standard of comparison. The analysis is performed in terms of analytical expressions, to make the characteristics of the different concepts more transparent. It is seen that the Japanese data are equally well fitted by a model that assumes no dependence of sensitivity on age at exposure but merely accounts for a dependence of the excess risks on dose and on age attained. This 'age attained model' corresponds, in essence, to formulations that have been used earlier for the analysis of lung cancers in uranium miners. The data up to 1985 for the atomic bomb survivors do not yet permit a decision between the different models. But the acceptability of the age attained model shows that age dependencies for leukaemias and other cancers to be less fundamentally different than commonly assumed. The age attained model leads to risk projections for young ages at exposure that are substantially lower than present estimates. In fact it predicts essentially the same lifetime attributable risk for exposures at young and intermediate ages; decreased risks result only for exposures at advanced ages where the expression periods are already substantially reduced.