Abstract: The object of the invention is to provide a method of operating a simply constructed centrifugal compressor equipped, in the region of the rear wall of the compressor impeller, with no sealing elements in the separating gap between the compressor impeller and the compressor casing, which method increases the service life of the centrifugal compressor. An appliance for carrying out the method is also to be made available. In accordance with the invention, this is achieved by introducing a cooling medium into the separating gap downstream of the leakage flow of the working medium and by finally removing this again after the cooling process has taken place. For this purpose, at least one supply duct for a gaseous cooling medium, the duct penetrating the compressor casing, opening into the separating gap in the region of the rear wall of the compressor impeller and directed onto the rear wall, and at least one removal duct for the cooling medium are arranged in the compressor casing.