Abstract: For impact grinding a free-flowing feed material to a finished product of a narrow grain size range, particularly in the cereal and feeding stuff grinding industry, the feed material is fed to an impact or hammer mill (1) having a sieve jacket (33), wherein it is subjected to a first impact grinding phase, during which a first finished product passes through the sieve jacket (33), while a recirculation material component is withdrawn from the grinding chamber (34) through exhaust means (51) provided on the sieve jacket (33), said recirculation material component being fed to a grain size separator means (4) comprising a sieve screen (44) for separating further finished product from an oversize component which is to be returned to the impact grinding phase, preferably together with newly introduced feed material.