The multistage milling machine uses gas eddies to comminute the material. The mill has a cylindrical stator (3) with a vertical shaft (1) on its centreline carrying the rotor. A feed device (15) at the top and an outlet (14) with a screw conveyor at the bottom. A carrier gas may be introduced through a passage opposite to the passage containing the screw conveyor. There are a large number of identical milling bodies (8) fastened to clamping rings (2) on the rotor on e.g. four levels. The milling action takes place in very small spaces between the outer diameters of the milling bodies and the inner diameter of the stator cylinder.