An apparatus for the comminution of suspended fibre materials is described in which the fibre material is led through milling gaps which are formed between rotor and stator surfaces occupied with milling tools. The rotor which is floatingly journalled at one end has two conical surfaces equipped with milling tools, with the conical surfaces cooperating with complementary counter surfaces of fixed location which are likewise equipped with milling tools to form radially spaced apart milling gaps which extend substantially over the same axial range, or axially sequential conical milling gaps which enlarge in diameter towards the center of the rotor.