The most recent update of the U.S. Environmental Protection Agency (EPA) health assessment document for asbestos (Nicholson, 1986, referred to as "the EPA 1986 update") is now 20 years old. That document contains estimates of "potency factors" for asbestos in causing lung cancer (K L 's) and mesothelioma (K M 's) derived by fitting mathematical models to data from studies of occupational cohorts. The present paper provides a parallel analysis that incorporates data from studies published since the EPA 1986 update.The EPA lung cancer model assumes that the relative risk varies linearly with cumulative exposure lagged 10 years. This implies that the relative risk remains constant after 10 years from last exposure. The EPA mesothelioma model predicts that the mortality rate from mesothelioma increases linearly with the intensity of exposure and, for a given intensity, increases indefinitely after exposure ceases, approximately as the square of time since first exposure lagged 10 years. These assumptions were evaluated using raw data from cohorts where exposures were principally to chrysotile (South Carolina Although the linear EPA model generally provided a good description of exposure response for lung cancer, in some cases it did so only by estimating a large background risk relative to the comparison population. Some of these relative risks seem too large to be due to differences in smoking rates and are probably due at least in part to errors in exposure estimates. There was some equivocal evidence that the relative risk decreased with increasing time since last exposure in the Wittenoom cohort, but none either in the South Carolina cohort up to 50 years from last exposure or in the New Jersey cohort up to 35 years from last exposure.textileThe mesothelioma model provided good descriptions of the observed patterns of mortality after exposure ends, with no evidence that risk increases with long times since last exposure at rates that vary from that predicted by the model (i.e., with the square of time). In particular, the model adequately described the mortality rate in Quebec chrysotile miners and millers up through >50 years from last exposure. There was statistically significant evidence in both the Wittenoom and Quebec cohorts that the exposure intensity-response is supralinear 1 rather than linear. The best-fitting models predicted that the mortality rate varies as [intensity] 0.47 for Wittenoom and as [intensity] 0.19 for Quebec and, in both cases, the exponent was significantly less than 1 ( p < .0001).Using the EPA models, K L 's and K M 's were estimated from the three sets of raw data and also from published data covering a broader range of environments than those originally addressed in the EPA 1986 update. Uncertainty in these estimates was quantified using "uncertainty bounds" that reflect both statistical and nonstatistical uncertainties. Lung cancer potency factors (K L 's) were developed from 20 studies from 18 locations, compared to 13 locations covered in the EPA 1986 update. Mesothelioma p...