The transport system has a fixedly arranged length of rail with two travel rails 5 which extend in the direction of travel and are transversely connected by means of crosspieces 15. A wheel flange-guided transport train consisting of a drive and brake vehicle 3 with transport vehicle 4 coupled thereto runs on the travel rails 5. In order to be able to use this wheel flange-guided transport train even in the region of steep sections of track, a guide rail 9d in which vertical and horizontal guide rollers 10 and 11 of the drive and brake vehicle 3 are supported is arranged between the travel rails 5. As a result, the drive and brake vehicle 3 is positively guided so that when braking on steep sections of track braking forces which exceed the drive and brake vehicle's 3 own weight can be applied without the risk of derailing or the wheels slipping. The drive is provided in the region of the steep section of track either by means of an externally operated traction cable 12 to which the drive and brake vehicle 3 is coupled or by a built-in drive, it then being possible for a toothed rack to be arranged on the section of rail and for a driven end wheel of the drive and brake vehicle 3 to engage in the said toothed rack. <IMAGE>