NOVELTY - The system has an indirect cooler (1) in which the material is cooled by direct contact with a surface of the cooler, a refrigeration system (2) for preparing a coolant for the cooler and a grinding device (4) for grinding the cooled material. A direct cooler (3) is arranged between the indirect cooler and the grinding device. DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for a method of operating the arrangement. USE - For cryogenic grinding of materials, especially for fine granulation. ADVANTAGE - Enables efficient and cost-effective cooling of the material to be ground.