A device for hands-free locking/unlocking of doors/windows of a vehicle implements at least two modes of operation: an approach-detection mode D and a tracking mode P. At least two antennas 14a, 14b are respectively coupled to amplifiers 12a, 12b that are active in tracking mode P. In approach-detection mode D the antennas are decoupled from the amplifiers used in mode P and coupled to an additional amplifier 12c that is active in mode D. Preferably, elements are provided to reduce the consumption of the amplifiers when the device is in a mode of operation where they are inactive.