Machines manufacturing pouches of a smokeless tobacco product or other cohesionless material, and systems for portioning and packaging tobamel type smoking mixtures, can be fitted with a flushing device that uses a number of spray nozzles (12, 31) positioned in close proximity to units (6, 30) by which the smokeless and smoking tobacco products are conveyed and processed; with the machine or system in operation, a cleansing fluid held in a tank (14, 33) is supplied under pressure to the nozzles (12, 31) by a pump (15, 34) and directed onto internal parts of the units (6, 30) in order to remove deposits of the product that tend to accumulate in the course of the processing steps, and thus avoid the need for frequent cleaning and maintenance stoppages.