Disclosed is an access device of a vehicle having an on-vehicle control device configured to transmit enquiry signals to a mobile identification transmitter to determine the state of motion thereof, and adapt the transmission of the enquiry signals for a response signal received from the mobile identification transmitter containing the state of motion of the mobile identification transmitter, or on the basis of the absence of the response signal. Energy is saved in the event of a response signal containing a communicated stationary state of the mobile identification transmitter or in the absence of a response signal by reducing the frequency of the transmission of the enquiry signals.