A binaural hearing aid system comprises left and right hearing instruments each comprising a BTE-part comprising a housing configured to be located at or behind an outer ear of the user and an acceleration sensor configured to measure acceleration in at least two directions relative to the housing of the BTE-part and to provide acceleration data indicative thereof. A first one of the left and right hearing instruments comprises a transmitter configured to transmit said acceleration data to the other hearing instrument, and the other hearing instrument comprises a receiver for receiving said acceleration data from the first one of the hearing instruments. The other hearing instrument further comprises a controller for detecting whether or not the left and right hearing instruments are correctly mounted in dependence of a similarity measure between said acceleration data provided by the left and right hearing instruments. A method of operating a binaural hearing aid system is further disclosed.