The invention pertains to a suspension conveyor system with a network of multiple rails and switches and a rolling apparatus that runs along this network. The rails have at least one sectional support girder (11) and two sectional run girders (8) of rectangular cross-section, each having an upper running surface (9). The sectional support girder (11) and the two parallel sectional running girders (8) are linked by mutually spaced webs such that a guide slit (7) of defined width is formed between the two sectional running girders (8). The rolling apparatus (4) has a carriage with two bearing rollers (5) of common running axis supported on the upper running surfaces (9) of the sectional running girders (8); below the guide slit (7) the rolling apparatus (4) is equipped with means for carrying a load, in particular a load-bearing hook (17), at the lower end of the carriage, the rolling apparatus (4) having just one running axis. Each sectional running girder (8) has a lower running surface. Below the bearing rollers (5) and engaging the sectional running girders (8) from below there are at least two stabilizing rollers (18) mounted at a distance from one another and behind the running axis of the bearing roller in the direction of travel of the rolling apparatus; the stabilizing rollers (18) run with their axes parallel to the axis of the bearing rollers, the stabilizing rollers (18) being supported on the lower running surfaces. The rolling apparatus (4) has two lateral guide rollers (6) mounted at a distance from each other in the running direction of the rolling apparatus, the axes of these guide rollers running perpendicular to the axis of the bearing rollers (5). The lateral guide rollers (6) are mounted between the bearing rollers and the stabilizing rollers (18) in such a way that they run following the guide slit (7) and cooperate with the switches.