The invention relates to a process and the associated device for the fine crushing of solid mineral and non-mineral substances, preferably cement raw materials and cement clinker, by single or repeated compressive-load application using medium to high pressures with subsequent disagglomeration of the produced ground material in the same device. The object of the invention is to create a crushing device which, under defined conditions of control of, and load application by, the material to be ground, combined in a single device, carries out several process steps in succession, continuously feeds the material to be ground, as a defined material layer, to the grinding gap formed from pressure roller and level load-application path and, through the free choice of grinding path speed and grinding pressure, has a favorable throughput behavior with a high energy utilization and low outlay on plant. This is achieved according to the invention in that the material to be ground is removed by gravimetric metered feed, as a defined material layer, from a feed container by the upper track, moved in translatory manner, of a plate conveyor guided continuously round a drive tumbler and reversing tumbler, suitably pre-crushed as required or subjected to some other preliminary process treatment, e.g. dried or wetted, in order to then be crushed under pressure by an elastically applied grinding roller and then disagglomerated in the same device by a fast-running striking mechanism.