The organic substance present in the form of a melt is cooled below its solidification point in a twin-screw extruder so that it crystallizes out. The crystallized material is then extruded through a breaker plate at the end of the screw extruder and further cooled. It is essential that the temperature prevailing in the screw extruder, its rotational speed and the temperature of the breaker plate should be adjusted such that from 70% to 99.5% and preferably from 95 to 99.5% of the material has solidified by the time it reaches the end of the screw, the non-crystallized liquid residue only crystallizing out during the subsequent cooling operation. Accordingly, a small residue of melt is present during extrusion through the breaker plate. In addition, extrusion is facilitated if the breaker plate is kept at a temperature in the vicinity of the melting point of the material in question.