Although the existence of a threshold in the dose effect relationship is well documented for many, if not most, types of toxicological effects the existence of a threshold for the mutagenic effects of ionising radiation and of certain chemicals has been questioned since the middle of the century and only recently the question of thresholds for radiation and chemical carcinogenesis has been addressed. The essential facts for the interpretation of threshold dose-response curves are common to all type of effects and are: (i) the number and the identity of the target; (ii) the type and sensitivity of the endpoint used to quantify the effect. We therefore will first try to model the type of interactions which may be expected between a mutagen and its target and define from this whether a threshold dose-effect can be expected; in a second step the concept will be extended to heritable mutations and carcinogenesis.