The system contains a code key (2) and a signal processor (6) connected to the closable part. The key exchanges code signals with the processor via transmission/reception devices, pref. bi-directionally, to cause locking or unlocking of the closable part by a controller. A first signal processor is mounted in the vehicle (4) to enable locking and unlocking of the doors (12). At least one further signal processor (6' ) can be mounted on a fixed building associated with the vehicle, e.g. a house (34) or garage (33), to enable the locking and unlocking of a door in the building. The signal exchange can take place between the key and the processor outside and inside the vehicle.