The form of the dose-response for induction of malignant diseases in vivo by ionizing radiation is not yet established in spite of its scientific interest and its practical importance. Considerably extended observations have confirmed that the dose-response for acute myeloid leukaemia induced in male CBA/H mice by X-ray exposure is highly curvilinear. The dose-response was well fitted by the expression aD/sup 2/esup(-..gamma..D) (D = dose) in agreement with induction at the cellular level in proportion to D/sup 2/ over the whole dose range 0.25-6.0 Gy. The factor esup(-..gamma..D) accounts for the inescapable concomitant inactivating action of the inducing irradiation. The quantitative aspects of induction of myeloid leukaemia by ionizing radiation are unlike the induction of genetic mutation or cell inactivation and suggest that interaction of two adjoining cells is an essential element in radiation leukaemogenesis.