The device includes a spray system for spraying a fluid against the inside periphery of the tube to be cleaned, and two analogous brushing assemblies, each of which include brushing means and a propelling element which cooperates with the inside periphery of the tube. The device further includes means for moving axially the brushing assemblies towards and away from each other in alternation, which means include a chamber connected to a feed for feeding in fluid under pressure. The spray system includes a reservoir put under pressure by being connected to the chamber. A method of cleaning a tube, in which two brushing assemblies including brushing means are inserted into the tube and are moved towards and away from each other in alteration. A fluid, disposed in a reservoir cooperating with a support system on which the propelling elements are secured, is sprayed against the inside periphery of the tube.