Multi-tank dishwashers are used, in particular, industrially, in order to clean items which are to be washed. The invention relates to a multi-tank dishwasher which is provided with a washing area. The washing area comprises at least one rinsing water storage tank, at least one filter housing, at least one fine filter and at least one backwash device. In the normal mode, a filter wall of the at least one fine filter is cross flown in the direction from a waste water chamber to a pure water chamber. In order to clean the fine filter, the multi-tank dishwasher can be operated in a backwashing mode, without interrupting the washing process. In said backwashing mode, a cross-flow of the at least one filter wall of the rinsing water is reversed by using a backwash pump and a waste water pump. Dirt particles, which are located on the inner side of the filter wall, are rinsed off and are removed by the waste water pump in the waste water outlet.