Carcinogenesis by α-particles has special features. Tissue irradiation is always inhomogeneous, sometimes extremely so. Tissue damage will be focal because cells out of reach of α-tracks (often the majority of cells) will not be irradiated at all. Since it is these unirradiated cells which allow tissue regeneration, random decay of radionuclides is a mechanism which increases nonhomogeneity of distribution of α-emitters in tissue as time progresses. Focal damage implies that cancer induction is linear with dose but, because the length of an α-track in tissue exceeds the dimensions of a single cell, linearity does not necessarily imply that malignant transformation is exclusively an intracellular process. Cellular inactivation of transformed cells will reduce the frequency of observed tumours and is easier to allow for than with low LET radiation because after high LET radiation there is no shoulder on the curve for retention of clonogenicity. With high LET radiation the dose response for carcinogenesis is sublinear, aDe −bD . When tissue exposures are protracted, cellular inactivation and tissue repopulation by means of cell division will proceed side-by-side throughout the exposure. Cellular repopulation will tend to neutralise the influence of inactivation on tumour frequency so that, as daily dose of protracted exposure decreases, observed tumour frequency may increase and become linear with dose. Human experience of carcinogenesis by α-emitters in bone and lung provides dose-responses compatible with linearity for induction, even in the case of Ra-226. In bone there may be quantitatively important age differences in sensitivity to sarcoma induction. Hepatic carcinogenesis by Thorotrast is an unsatisfactory model for other α-emitters because in virtually all subjects bearing Thorotrast the liver is structurally abnormal as a consequence of tissue damage. The linear risk coefficient for Thorotrast-induced malignant disease originating in bone marrow (mostly leukaemia) and for death from bone marrow failure implies that RBE for comparisons with low LET radiation is small 1–3. This may not be unreasonable since α-irradiation of the marrow will have been largely focal, leaving many marrow cells unaffected. However an alternative possibility is that cellular inactivation has led to a falsely low value for the risk coefficients for α-irradiation by Thorotrast. Deeper understanding of observations on Thorotrast subjects and application of them to problems of human exposure to other α-emitters, such as plutonium, require (a) subdivision of subjects according to volume of Thorotrast injected, so that dose response relationships may be examined directly without reliance on the assumption of linearity, and (b) decisive experiments to show whether chemical toxicity as well as α-radioactivity contributes to tissue damage and induction of cancer.