A system for the registration of radiation images has a radiation pick-up device and a control device controlling the operation thereof. The radiation pick-up device has a charge layer that generates electrical charges dependent on the incident radiation and an allocated electrode layer that is chargeable with high-voltage for triggering an electron-multiplying avalanche effect in the charge layer by virtue of a potential produced across the charge layer by the high-voltage. A read-out device reads out the generated charges in the charge layer by means of an electron beam. The potential via the charge layer can be modulated for varying the gain of the charge layer caused by the avalanche effect.