In cold grinding, the materials to be ground are cooled and embrittled with cryogenic liquid nitrogen or carbon dioxide. This method achieves particularly high grain fineness while maintaining product quality. In addition, the mill throughput is significantly increased. In particular, cooling the grinding process with cryogenic gases in the case of heat-sensitive substances prevents a rise in temperature which results from the conversion of the electrical energy of the mill motors. This prevents melting and sticking of the ground material.