To date, the analysis of mutation induction has provided an irrefutable evidence for an elevated germline mutation rate in the parents directly exposed to ionizing radiation and a number of chemical mutagens. However, the results of numerous publications suggest that radiation may also have an indirect effect on genome stability, which is transmitted through the germ line of irradiated parents to their offspring. This review describes the phenomenon of transgenerational instability and focuses on the data showing increased cancer incidence and elevated mutation rates in the germ line and somatic tissues of the offspring of irradiated parents. The possible mechanisms of transgenerational instability are also discussed.