Time signals for controlling a radio clock are transmitted by a transmitter and received by a receiver as amplitude modulated time signals, formed of a multitude of time frames. Each time frame has a constant duration. These time signals are first automatically amplified. A so-called telegram of at least one received time signal is stored in a memory. At least one change of an amplitude of a time signal is determined in advance or predetermined and such amplitude change has a duration that is longer than a given or determined duration (.DELTA.t). When a predetermined amplitude change begins the automatic amplification is locked-in. The present circuit arrangement for operating a radio-controlled clock is equipped with components for performing the foregoing operations.