Mortality reports on asbestos exposed cohorts which gave information on exposure levels from which (as a minimum) a cohort average cumulative exposure could be estimated were reviewed. At exposure levels seen in occupational cohorts it is concluded that the exposure specific risk of mesothelioma from the three principal commercial asbestos types is broadly in the ratio 1:100:500 for chrysotile, amosite and crocidolite respectively. For lung cancer the conclusions are less clear cut. Cohorts exposed only to crocidolite or amosite record similar exposure specific risk levels (around 5% excess lung cancer per f/ml.yr); but chrysotile exposed cohorts show a less consistent picture, with a clear discrepancy between the mortality experience of a cohort of xhrysotile textile workers in Carolina and the Quebec miners cohort. Taking account of the excess risk recorded by cohorts with mixed fibre exposures (generally<1%), the Carolina experience looks uptypically high. It is suggested that a best estimate lung cancer risk for chrysotile alone would be 0.1%, with a highest reasonable estimate of 0.5%. The risk differential between chrysotile and the two amphibole fibres for lunc cancer is thus between 1:10 and 1:50. Examination of the inter-study dose response relationship for the amphibole fibres suggests a non-linear relationship for all three cancer endpoints (pleural and peritoneal mesotheliomas, and lung cancer). The peritoneal mesothelioma risk is proportional to the square of cumulative exposure, lung cancer risk lies between a linear and square relationship and pleural mesothelioma seems to rise less than linearly with cumulative dose. Although these non-linear relationships provide a best fit ot the data, statistical and other uncertainties mean that a linear relationship remains arguable for pleural and lung tumours (but not or peritoneal tumours). Based on these considerations, and a discussion fo the associated uncertainties, a series of quantified risk summary statements for different elvels of cumulative exposure are presented.