In vitro studies show that protective tumour-reducing effects occur for low dose rates (mGy per minute). To account for these phenomena, we have previously developed stochastic and deterministic multi-stage cancer models that include radiation-induced adaptations in DNA repair processes and radical scavenging. Here, these models are extended to account for the induction of radioprotective mechanisms for low doses of low LET radiation delivered at high dose rates. Cellular adaptations in DNA repair are related to temporal changes in the amount of DNA damage in a cell. The combined effects of endogenous DNA damage, background radiation and artificial irradiation are considered.