A new model (Random Coincidence Model--Radiation Adapted (RCM-RA)) is proposed which explains a possible pseudo threshold for stochastic radiation effects. It describes the formation of cancer in the case of multistep fixation of lesions in the critical regions of tumor associated genes such as proto-oncogenes or tumor-suppressor genes. The RCM-RA contains two different possibilities of DNA damage to complementary nucleotides. The damage may be caused either by radiation or by natural processes such as cellular radicals or thermal damage or by chemical cytotoxins. The model is based on the premise that radiation initially is bionegative, damaging organisms at their different levels of organization. The radiation, however, also induces various cellular radioprotective mechanisms which decrease the damage by natural processes. Considering both effects together, the theory explains apparent thresholds in the dose-response relation for radiation carcinogenesis without contradiction to the classical assumption that radiation is predominantly bionegative at doses typically found in occupational exposures.