The invention provides a device for measuring ionizing radiations, comprising a Geiger-Muller tube (1) whose high supply voltage is obtained from pulses which are emitted (by 6,7) at a constant relatively low frequency as long as a predetermined threshold is not exceeded by the intensity of the radiation and (by 6,7,4 and 32) at an increasing frequency depending on the output of the tube, after said threshold has been exceeded. Thus, alarm dosimeters having very long independent operation may be formed.