This study aims to investigate the contribution of diagnostic exposures to the rising rates of brain tumours and other neoplasms which are observed in several industrial nations. Included are benign tumours in the head and neck region and cataracts which are neglected in usual risk estimates by international and national radiation protection committees. 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. Risk estimates are derived for paediatric head computed tomographies (CTs) as well as for brain tumours in adults. On the basis of estimates for Germany about the number of head scans, the annual rate of radiation-induced diseases is calculated. About 1000 annual paediatric CT investigations of the skull will lead to about three excess neoplasms in the head region, i.e. the probability of an induced late effect must be suspected in the range of some thousands. 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.