The application relates to a binaural hearing system comprising left and right hearing devices, e.g. hearing aids, each comprising a) a multitude of input units, each providing a time-variant electric input signal xi(t) representing sound received at an ith input unit, t representing time, the electric input signal xi(t) comprising a target signal component si(t) and a noise signal component vi(t), the target signal component originating from a target signal source; b) a configurable signal processing unit for processing the electric input signals and providing a processed signal y(t); c) an output unit for creating output stimuli to the user, d) transceiver circuitry allowing information to be exchanged between the hearing devices, and e) a binaural speech intelligibility (SI) prediction unit for providing a binaural SI-measure of the predicted speech intelligibility of the user when exposed to said output stimuli, based on processed signals yl(t), yr(t) from the signal processing units of the respective left and right hearing devices. This allows the hearing devices to control the processing of the respective electric input signals based on said binaural SI-measure.