Data from inhalation studies in which AF/HAN rats were exposed to nine different types of asbestos dusts (in 13 separate experiments) are employed in a statistical analysis to determine if a measure of asbestos exposure (expressed as concentrations of structures with defined sizes, shapes and mineralogy) can be identified that satisfactorily predicts the observed lung tumor or mesothelioma incidence in the experiments. Due to limitations in the characterization of asbestos structures in the original studies, new exposure measures were developed from samples of the original dusts that were re-generated and analyzed by transmission electron microscopy using a direct transfer technique. This analysis provided detailed information on the mineralogy (i.e., chrysotile, amosite, crocidolite or tremolite), type (i.e., fiber, bundle, cluster, or matrix), size (length and width) and complexity (i.e., number of identifiable components of a cluster or matrix) of each individual structure. No univariate measure of exposure was found to provide an adequate description of the lung tumor responses observed among the inhalation studies, although the measure most highly correlated with tumor incidence is the concentration of structures > or = 20 microns in length. Multivariate measures of exposure were identified that do adequately describe the lung tumor responses. Structures contributing to lung tumor risk appear to be long (> or = 5 microns) thin (0.4 microns) fibers and bundles, with a possible contribution by long and very thick (> or = 5 microns) complex clusters and matrices. Potency appears to increase with increasing length, with structures longer than 40 microns being about 500 times more potent than structures between 5 and 40 microns in length. Structures < 5 microns in length do not appear to make any contribution to lung tumor risk. This analysis did not find a difference in the potency of chrysotile and amphibole toward the induction of lung tumors. However, mineralogy appears to be important in the induction of mesothelioma with chrysotile being less potent than amphibole.