[en] With the Random Coincidence Model (RCM) it is possible to explain the radiobiological effect of radiation hormesis, the decrease of certain tumor mortality rates with increasing annual dose within the lowest annual dose regions. The RCM describes the formation of cancer if caused by a multistep series of fixed lesions in the critical regions of tumor associated genes such as proto-oncogenes or tumor-suppressor genes. It is the central subject of the model that for lowest annual doses a fixed DNA-damage mainly occurs through the random coincidence of two base lesions on complementary DNA bases during the repair time of the first base lesion. The RCM also describes the stimulation of cellular defense mechanisms by small annual doses of ionizing radiation. The solutions of coupled differential equations are applied to two different data sets referring to high-LET and low-LET radiation. The-data are provided by B.L. Cohen and by ARIP. Nonlinear regression analysis leads to a hormetical dependence, both for lung cancer and for the sum of all cancers. The resulting thresholds for stochastic effects are in the range of natural background. The fit-results are explained biologically and are recalculated. (author)