A method for operating an authorization device for keyless entry and starting of a vehicle with a portable ID transmitter that has a motion sensor. A wireless communication link for interchanging data messages can be set up between the authorization device and the ID transmitter. Keyless entry to the vehicle is permissible only when an instant of last movement of the ID transmitter, as captured by the motion sensor, is within a stipulated interval of time. The authorization device permits keyless starting of the vehicle only when keyless entry to the vehicle has previously been permitted.