A new binaural hearing aid system is provided with a hearing aid in which signals that are received from external devices, such as a spouse microphone, a media player, a hearing loop system, a teleconference system, a radio, a TV, a telephone, a device with an alarm, etc., are filtered with binaural filters in such a way that a user perceives the signals to be emitted by respective sound sources positioned in different spatial positions in the sound environment of the user, whereby improved spatial separation of the different sound sources is facilitated.