Abstract: The invention relates to a method for grinding mill material and to a roller mill and is suited in particular to a finest grinding of relatively hard and dry materials, for example cement clinker and granulated blast furnace slag and also for relatively large roller mills. In order to avoid mill vibrations due to over-grinding of the mill material and to reduce the specific work requirement as well as increasing the throughput a fine material nozzle is arranged after each grinding roller, from which fine material nozzle an air jet with defined impulse is directed from above onto a fine material concentration zone. The fine material concentration zone is formed directly after the grinding zone of each grinding roller and is virtually free of supplied material to be ground and accumulated on a retention rim region. The fine material blown outwards and upwards is fed to a rising conveying air flow and subsequent classifying process.