The absence of threshold in the action of genotoxic carcinogens was theoretically postulated more than thirty years ago, but continuously challenged for scientific and practical reasons. The direct experimental demonstration of the presence of a threshold for genotoxic damage is precluded by the insufficient sensitivity of the biological methods presently available. In the last twenty years the sensitivity of the methods for quantitative determination of the DNA adducts of the carcinogens was enormously improved, demonstrating linearity of the dose/adducts pattern over dose intervals of more than million-fold. The arguments more often advanced for the presence of a threshold for genotoxic carcinogens were mainly based on the action of intracellular scavengers, detoxification enzymes and repair systems, being able to block completely the genotoxic carcinogens at very low doses. This hypothesis is disproved by the constant presence of DNA adducts at extremely low doses of different carcinogens, whatever their chemical structure can be. On the other hand if genotoxic damage results from damage to proteins involved in cell division, like tubulin, there is a threshold dose for such genotoxic effects. The detailed knowledge of the genotoxicity mechanism is therefore needed for a sound carcinogenic risk assessment. Most of the genotoxic carcinogens, or their metabolites, damage directly the DNA. In this case the absence of threshold must be assumed, not only for theoretical reasons, but for the results of the experiments quantitatively relating DNA damage and very low doses of carcinogens. For the sake of clarity the "adjectivated" thresholds, like practical pragmatic, apparent and operational, must disappear from documents analysing the carcinogenic risk.