A centrifuge having a drum rotatable in a predetermined direction about a drum axis has a cleaning device with a cleaning shaft extending generally parallel to the drum axis into the drum along a shaft axis. A pair of elongated slat-shaped cutters have inner ends fixed on the shaft, outer ends, and project radially outward of the shaft axis from the shaft. The inner ends are separated by a relatively narrow space, and the cutters diverge from their inner ends toward their outer ends. The shaft can be moved such that the cutters are displaced between a standby position offset from the drum and a cleaning position closely juxtaposed therewith. A cleaning liquid is fed to each cutter such that it flows along the cutters.