The invention describes a method for operating a device for monitoring and wireless signalling a pressure or a pressure change in pneumatic tires of wheels on vehicles, the device being hereinafter referred to as wheel electronics, wherein the pressure prevailing in the pneumatic tire is measured and electric pressure signals are derived from such measurements, and an information signal containing information on the pressure or on a pressure change is transmitted, the information signal being intended to be received by a receiver provided in or on the vehicle, the wheel electronics being set by a first control signal, which is transmitted in wireless fashion from outside the wheel electronics, to a first mode of operation in which the prevailing pressure or a pressure change is measured and signalled in response to the receipt of an interrogation signal generated outside the wheel electronics and transmitted to the wheel electronics in wireless fashion, and, if the wheel electronics do not receive another interrogation signal within a predetermined period of time after receipt of an interrogation signal, the wheel electronics adopting itself a second mode of operation in which the pressure or a pressure change is measured repeatedly and is transmitted at a transmission rate which is firmly preset or is variable and which is established in the wheel electronics for that second mode of operation.