An apparatus for cleaning wafers using the CMP process includes a transport device of a feeding station at the beginning of a cleaning line which has a plurality of transport rollers disposed and driven transversely to the direction of transport. The cleaning line transports polished wafers to a main cleaning station having several pairs of transport rollers for transporting the wafers through the main cleaning station and several pairs of cleaning rollers for cleaning the wafers, wherein a supply of a cleaning medium to the pairs of cleaning rollers is provided in the main cleaning station. A withdrawal station is disposed at the end of the cleaning line in which a robot takes up a wafer and transports it to a drying station, wherein the withdrawal station has a first detector. A water cushion transport line is disposed between the main cleaning station and the withdrawal station and a stop station is disposed between the main cleaning station and the withdrawal station which has associated thereto a second detector. A control device presets a predetermined ratio of the speed of the transport rollers of the transport device and that of the pairs of transport rollers of the main cleaning station and does not release a transport to the feeding station until there is no wafer at the stop station, and releases a wafer to the withdrawal station only when there is no wafer therein.