The invention relates to a pull-in system for multiple pull-out furniture parts (1), each of which can be pulled out of a furniture body (30) in a pull-out direction (44) and inserted into the furniture body (30) in a direction opposite the pull-out direction. The pull-in system comprises a pull-in unit (7) for each of the pull-out furniture parts (1). Each pull-in unit has a pull-in part (5) which is urged by a retracting spring (27) and which can be adjusted between a normal position and a standby position by a driver (2), wherein the driver (2) uncouples from the pull-in part (5) when the pull-out furniture part (1) is pulled out in the standby position, and each pull-in unit has a bearing unit (8) which supports the pull-in part (5) in a movable manner between the normal position and the standby position. The pull-in system further comprises at least one mounting rail (29) which can be fixed to the furniture body (30) and which has multiple mounting spaces (61). Each of the bearing units (8) can be fixed to a respective mounting space (61), and for this purpose each mounting space (61) has at least one mounting element (64, 65, 70, 71, 72, 77) for fixing the bearing unit (8) on the mounting rail (29). The bearing units (8) can be connected to the mounting rail (29) via snap-on connections.