A machine for making liquid or semi-liquid food products, specifically ice cream, includes a vessel for processing liquid or semi-liquid base products by means of a stirring device driven by a motor. The mixture in the vessel is transferred through a duct, along which movement means for moving the mixture are operatively located, these movement means comprising a rotary device including two juxtaposed discs, on which a series of rollers is mounted in such a way as to press a flexible portion of the duct, and an opposing element confronting the rollers.