A anti-theft system is provided which prevents a vehicle equipped with the system from being driven away more than a predetermined distance. The system includes a first electronic control device which is mounted in the vehicle which control continued operation of the vehicle after the vehicle is started, e.g., controls opening of the ignition or fuel injection circuits. A second electronic control device, adapted to be worn by a person authorized to use the vehicle, receives a characteristic signal from the first device and transmits a return signal in response thereto. A control circuit of the first device calculates the distance between the two devices based on the returned signal and disables vehicle operation when the distance is greater than the predetermined distance.