1. Railway ballast cleaning machine adapted to travel on rails, with a vibrating screen arrangement (15) for cleaning the ballast, preferably with two spaced superposed perforated bottoms (40, 41), and with belt conveyors (13, 14, 28, 29) for transporting the ballast and the waste, characterized in that the vibrating screen arrangement (15) comprises at least two vibrating screens (16, 17 ...