AbstractThe principle of tolerance to injurious substances and the use of threshold limit values have been central to the practice of occupational health. The concept of a threshold is well established in biological processes, for example, synaptic transmission and nerve stimulation as well as for acute effects of chemicals and radiation. Obviously, the protection of both the worker and general population would be greatly simplified if thresholds for carcinogenesis also existed and could be determined. Unfortunately, thresholds for carcinogenesis are like leprechauns, it is difficult to demonstrate their existence, but they generate lively if not always completely rational discussions.