Mesothelioma death rates in asbestos workers appear to be proportional to the 3rd or 4th power of time from first exposure under a wide range of conditions of exposure for both pleural and peritoneal tumours, though the peritoneal:pleural ratio depends on fibre dimension and type. Age at first exposure has little or no influence, however, which supports the "multi-stage" model of carcinogenesis under which the increase in most cancer incidence rates with age is due to a constant incidence of genetic or epigenetic accidents, rather than to progressive generalized changes in regulatory or immune function. These relationships provide a simple basis for risk assessment, and support the suggestion that mesotheliomas may constitute a high proportion of cancer deaths resulting from early exposure to asbestos.