The process for cleaning the filter modules (13) of a cross-flow filter device is performed in a plant used to purify liquids, especially those with a high fibre content. The problem here is the continuous collection of fibres, especially at the inlet to the filter modules (13) at the fronts of the individual channels, which can lead to blockages. To remove the collections of fibres, the direction of flow in the module (13) during cleaning is the reverse of that in the previous filtration cycle. This is achieved by suitably switching valves (9 to 12). The reversal of the direction of flow means that the collections of fibres, which are still small, can easily be removed and rinsed out of the modules. Blockages of the modules can thus be prevented.