Vehicle intended for travelling along at least one rail

The vehicle has synchronizing units (58) for synchronizing the movements of sustentation modules (5, 6, 7, 9) of a sustentation device. The units have a hydraulic jack (59) interposed between the modules (5, 7) and a case (3), a hydraulic jack (60) interposed between the modules (6, 9) and the case, and a fluidic circuit (64) connecting the jacks (59, 60) for synchronizing the actions of the jacks.