A locking system includes at least one electrical locking member for a door and at least one key member. Each electrical locking member is associated with a first communication member for wireless communication over short distances, and each key member includes a programmable, mobile unit including a second communication member for wireless communication over short distances. The electrical locking member is unlocked or locked by the fact that the second communication member encryptedly transmits an address unique to the second mobile unit, as well as an authorized user code to the first communication member.