Existing systems of classification of carcinogens are a matter of discussion, world-wide. There is agreement that it should be distinguished between genotoxic and non-genotoxic chemicals. The risk assessment approach used for non-genotoxic chemicals is similar among different regulatory bodies: insertion of an uncertainty (safety) factor permits the derivation of permissible exposure levels at which no relevant human cancer risks are anticipated. For genotoxic carcinogens, case studies of chemicals point to a whole array of possibilities. Positive data of chromosomal effects only, in the absence of mutagenicity, may support the characterization of a compound that produces carcinogenic effects only at high, toxic doses. Non-DNA-reactive genotoxins, such as topoisomerase inhibitors or inhibitors of the spindle apparatus are considered in this respect. In such cases, arguments are in favour of the existence of "practical" thresholds. Taking existing concepts together, it is proposed to basically distinguish between "perfect" and "practical" thresholds. There is a wide consensus that for non-DNA-reactive genotoxins such as aneugens (aneuploidy, chromosome loss, non-disjunction) thresholds should be defined. It is being discussed as to whether the identification of possible threshold effects should also include other mechanisms of genotoxicity, in addition to aneugenic effects. Specific mechanisms of clastogenicity have been repeatedly addressed as also having thresholds, such as topoisomerase II poisons or mechanisms based on reactive oxygen. Oxidative stress as an important mechanism is triggered by exposure to exogenous factors such as ultraviolet (UV) and ionizing radiation, anoxia and hyperoxia, and by chemicals producing reactive oxygen species. The idea is receiving increased support that reactive oxygen species (ROS)-mediated processes of carcinogenesis have practical thresholds. Since reactive oxygen species are genotoxic in principle, questions arise whether chemicals that increase ROS production will superimpose to an endogenously produced background level of DNA lesions, related to mechanisms that may result in non-linear dose-effect relationships. The existence of "endogenous" DNA adducts has been generally accepted, and possible regulatory implications of the presence of endogenous carcinogens have been discussed. It is now becoming evident that a diversity of methods of carcinogenic risk extrapolation to low doses must be considered, dependent on the mode of action. Although there is an increasing international awareness of these developments, the system of classification of carcinogens of the European Union still remains static. This should be changed, as the philosophy of separation of a strictly sequential "hazard assessment" and "risk assessment" appears out-of-date.