To provide a binaural hearing aid system which preserves directional cues in received sound signals.

Each of a first hearing aid and a second hearing aid comprises: a microphone and an A/D converter for providing a digital input signal in response to received sound signals; a compressor for compensating for dynamic range hearing loss on the basis of a signal level; a processor that is configured to process the digital input signal into a processed digital output signal in accordance with a selected signal processing algorithm; a D/A converter and an output transducer for converting the processed digital output signal into an acoustic output signal; and a transceiver 22 for data communication with the other hearing aid. A gain of the compressor of the first hearing aid is controlled by a signal having a value that is substantially equal to a value of a signal controlling a gain of the compressor in the second hearing aid, whereby a sense of direction is maintained.