A hearing system and a method for operating a binaural hearing system include at least two hearing devices to be at least partly inserted into or to be worn behind the left and right ear of a user. Each hearing device includes at least one microphone to generate an electrical signal corresponding to an acoustic signal. The method includes determining contra-lateral information based on an acoustic signal recorded by a microphone of the contra-lateral hearing device, and determining ipsi-lateral information based on an acoustic signal recorded by a microphone of the ipsi-lateral hearing device. The method includes providing a coordination level, the coordination level being indicative of a degree of synchronization of the two hearing devices, and adjusting processes in the ipsi-lateral hearing device in accordance with the coordination level. The coordination level can be determined from the contra-lateral information and/or from the ipsi-lateral information, or be obtained from an external device.