600657 Disclosed is a filtration system (4) and method for filtering a cloudy beverage such as a cloudy wine from at least one tank (1) in which dregs have formed using cross-flow filtration. The system (4) comprises a first filtration circuit (11) and a second filtration circuit (12) in parallel. The first (11) and second (12) filtration circuits each comprise a filtration module (6, 7) having at least one or more filtration elements. Each filtration element comprises channels (9, 10). The diameter of the first filtration element channels are less than 2mm. The diameter of the second filtration channels is greater than 6mm. The system further comprises a supply line (25) for a fluid preferably an inert gas and a common discharge line (26).