A conveying apparatus (1) moves a transport unit (3) having at least one running section (4, 5). The running section (4, 5) can, in particular, be configured as a runner of a skid. The conveying apparatus (1) has a support (6, 8) which takes up the weight of the transport unit (3) on the running section (4, 5). The conveying apparatus (1) includes at least one drive roller (20) which interacts with the running section (4, 5) of the transport unit (3) for a rolling movement and subjects the transport unit (3) to a force (FK) for movement along the support (6, 8). The drive roller (20) is operatively connected to a force-generating device (44) for providing a press-on force (FP) pressing the drive roller (20) against the running section (4, 5) of the transport unit (3).