The system has a uniform system architecture that is designed for an access authorization request both with and without the use of a transponder. Should a transponder be used, only a corresponding transponder must be fitted in the key that can interact with an immobilizer coil specially provided for this in a receiving unit of the motor vehicle. In this case, the corresponding system requirements have also already been taken into consideration in the system architecture. As a result, the different system requirements for access and right of use systems to a great extent provide flexibility.