A complete assessment of late effects of X-ray diagnostics should take into account that radiation sensitivity varies considerably for the different ages at exposure and, furthermore, that not only malignant diseases but also benign neoplasms are induced which also may lead to severe detriment of the patient. Risk estimates are derived for paediatric head CTs as well as for brain tumours in adults. Dose-effect relationships for tumours of the brain, skin, thyroid, and other sites of the head region, leukaemia, and cataracts are taken from the literature. On the basis of estimates for Germany about the number of head scans, the annual rate of radiation-induced diseases is calculated. 1 000 annual paediatric CT investigations of the skull will lead to about 3 excess neoplasms in the head region, i.e., the probability of an induced late effect must be suspected in the range of some thousandths. Additionally, a relevant increase of cataracts must be considered. The radiation-induced occurrence of meningiomas and other brain tumours most probably contributes to the continuously increasing incidence of these diseases which is observed in several industrial nations, as well as the exposure of the bone marrow by CT to the increase of childhood leukaemia.