A transport system suitable for the transport of buckets in a combination weighing machine that comprises a first and a second endless chain drive (2, 3), each one defining a closed path with a horizontal straight upper advance section (2c, 3c), a lower horizontal straight return section (2d, 3d) and respective curved sections (2a; 2b; and 3a; 3b) around corresponding centers of the curvature r that link the mentioned advance and return sections,, the first and second chain drives (2, 3) arranged parallel to each other but horizontally offset at a distance A, the system further comprising a series of carriages that carry the buckets which extend between the chains (2, 3) and which are connected in an articulated way to the chains by joining arms (52, 53) that are horizontally offset at the same distance A, such that the simultaneous and coordinated motion of the first and second chains makes the carriages move along a closed path in which are distinguished a horizontal straight upper advance section, a lower horizontal straight return section and curved sections linking the mentioned advance and return sections, the system comprising control gears to controlling the inclination of the carriages on the curved sections of its path, which comprise castor wheels (72a, 72b) that are operable in a coordinated fashion with the chains (2, 3) around corresponding turn axes n, being placed at least one of them in the vicinity of each curved section of the carriages path and prepared to mesh with contact elements arranged for such purposes in the carriages, all of which in a way so that on said curved sections the inclination of each carriage is conditioned by the meshing that occurs between at least one of its contact elements and a castor wheel, - wherein the contact elements comprise a set of protrusions (62a; 62b) arranged in the carriages and configured to mesh in corresponding recesses provided in the castor wheels (72a, 72b), the system being characterized in that the number of castor wheels (72a; 72b; 73a; 73b) being four, each one located in the vicinity of each curved section (2a; 2b; 3a; 3b) of each chain (2, 3), each carriage is equipped with a first and a second gear end (42, 43), to mesh with a corresponding castor wheel, each one having a pair of protrusions (62a and 62b; 63a and 63b) - arranged in the advanced direction of the carriage one on each side of the joining arm (52, 53) that connects each carriage to a chain (2, 3) and equidistant from said joining arm at the same horizontal distance C, - arranged at a different level with respect to said joining arm (52, 53) one on top and another below the one on top, equidistant from said joining arm at the same vertical distance B; - of which at least one in each gear end (42, 43) in each curved path of the carriage cooperates with a recess of the castor wheel (72a; 72b; 73a; 73b) located in the corresponding curved section (2a; 2b; 3a; 3b) of the associated chain (2, 3); and in that the turn axis n of the castor wheels (72a; 72b; 73a; 73b) that cooperates with the aforementioned protrusions (62a and 62b; 63a and 63b) are horizontally offset at the same distance C and vertically offset at the same distance B with respect to the center of curvature r of the curved sections of their associated chains. - wherein the contact elements comprise a set of protrusions (62a; 62b) arranged in the carriages and configured to mesh in corresponding recesses provided in the castor wheels (72a, 72b), the system being characterized in that the number of castor wheels (72a; 72b; 73a; 73b) being four, each one located in the vicinity of each curved section (2a; 2b; 3a; 3b) of each chain (2, 3), each carriage is equipped with a first and a second gear end (42, 43), to mesh with a corresponding castor wheel, each one having a pair of protrusions (62a and 62b; 63a and 63b) - arranged in the advanced direction of the carriage one on each side of the joining arm (52, 53) that connects each carriage to a chain (2, 3) and equidistant from said joining arm at the same horizontal distance C, - arranged at a different level with respect to said joining arm (52, 53) one on top and another below the one on top, equidistant from said joining arm at the same vertical distance B; - of which at least one in each gear end (42, 43) in each curved path of the carriage cooperates with a recess of the castor wheel (72a; 72b; 73a; 73b) located in the corresponding curved section (2a; 2b; 3a; 3b) of the associated chain (2, 3); and in that