So as to put binaural beam-forming into practice selected acoustical situations are dealt with having minimum processing power and power consumption ability at a binaural hearing system. For near-to-ear acoustical sources the contra-lateral (7L) as well as the ipsi-lateral (7R) output electrical-to-mechanical converters of two hearing devices of the binaural hearing system are operated substantially exclusively in dependency from the output signal of the one ipsi-lateral input acoustical-to-electrical converter arrangement (3R).