A transport system designed to transport buckets in a combination weighing machine that uses two endless chain drives horizontally offset at a distance A, the system comprising carriages to carry the buckets which extend between, and are joined to, the chains such that the simultaneous and coordinated motion of the chains moves the carriages along a closed path with curved sections, the system comprising control gears for the inclination of the carriages on the curved sections of the path, which comprise castor wheels actuated in a coordinated fashion with the chains around both turn axes n, at least one of which placed in the vicinity of each curved section linking the carriages and prepared to mesh with contact elements arranged for such purposes on the carriages.