A system includes an installation to be cleaned which has at an inlet a fluid feed pipe fed with fluid and at an outlet a fluid evacuation pipe. A cleaning device is arranged to cause cleaning bodies to flow in the installation, the cleaning device including on an inlet filter elements for filtering the fluid and on an evacuation pipe separator elements for collecting the cleaning bodies. The separator and filter elements are static and include separate filters, the separator elements including a filter member, the cleaning device including a circuit for recovering cleaning bodies circulating in the evacuation pipe and a circuit for reinjecting them into the inlet, the two circuits having in common the filter member and being used alternately by actuating a set of controlled valves in order to cause the fluid to flow either in the recovery circuit or in the reinjection circuit.