A binaural healing system includes a left-ear hearing device, a right-ear hearing device and an auxiliary device. The auxiliary device has a connected mode wherein it transmits data messages and a disconnected mode wherein it does not transmit data messages, and the auxiliary device is adapted to enable the connected mode in dependence on receiving beacon messages, to synchronize its transmission of data messages with received beacon messages and to enable the disconnected mode in dependence on not receiving beacon messages. To avoid disconnection of the auxiliary device S during gaps, the left-ear hearing device and the right-ear hearing device are adapted to alternatingly transmit the beacon messages.