It has long been accepted that excessive exposure to asbestos may produce lung cancer but not that there is a consistent "biological gradient." This can only be evaluated reliably in studies where, for every individual, exposure has been measured in terms of both duration and intensity. Even now, there are only at most eight such cohort studies of asbestos workers, while femoral methods of analysis have been available only recently. These methods, applied in these studies, yield good evidence that the "exposure-response" relation between accumulated exposure to asbestos and standardised mortality ratios (SMRs) for lung cancer may be taken as linear, but that at zero exposure the lung cancer SMR is not always unity--not surprising, because of well known difficulties with the choice of reference population and selection problems. This leads to a concept of "relative slopes" that take account of the background mortality in the cohort and make what appears to be the best use of the available data. Other approaches to the same data, and indeed to all cohort data known, are also considered. Each study is examined as closely as is possible in a short review, and the concepts of linearity and relative slopes appear justified. The relative slopes (b/a) in the line SMR = a[1 + (b/a) . (exposure)] vary much more widely than can be accounted for by differences in epidemiological methodology; as discussed elsewhere, reasons for the variation seem to lie rather in type and dimensions of asbestos fibre, industrial process, etc. Slopes in the line SMR = 1 + b1 . (exposure) vary about twice as much as do the relative slopes.