The rail-based conveyor system is equipped with a self-propelled chassis (6) which has at least one friction wheel (20) and/or gearwheel (22), which interact or interacts with a rail (2) and can be driven by a motor (28), as well as a load bearer (40). With respect to a horizontal arrangement, the rail (2) is designed and arranged with an upright cross section, and the chassis (6) is arranged essentially at the side of the rail (2). The chassis (6) is supported on the rail (2) by upper and lower wheels (8, 10) which absorb lateral forces, and further wheels (16) which absorb vertical forces. The load bearer (40) is arranged on the chassis (6) on the side facing away from the rail (2) and such that it can pivot about an axis (42) aligned at right angles to the plane of the rail (2). An improvement to the conveyor system in particular with regard to the physical height is achieved in that the rail (2) has on the upper face a U-shaped profile (12), which is open at the top, for the upper wheels (8) and on the lower face has a U-shaped profile (14) which is open at the bottom, for the lower wheels (10), in order to absorb the lateral forces, as well as a U-shaped profile (18), which is open at the side with respect to the chassis (6, 6a), for further wheels (16) in order to absorb the vertical forces, with the wheels being in the form of running wheels.