Anti-theft system for a motor vehicle and method for operating an anti-theft system

An anti-theft system comprises a transmitter and receiver unit (20) in the motor vehicle (10), the radar emits signals broadband-modulated and then waits for the echo signals. A code generator (30) receiving a radar signal, in turn sends back an additional modulated and coded signal. An evaluation unit analyzes all the received echo signals on the one hand to an authorization of the code transmitter (30) and on the other hand with regard to the distance between the code transmitter (30) and transmitting and receiving unit (20).