For reel core disposal from a reel stand (1) of a row of reel stands, a conveyor belt (21) running along said row is arranged on the removal side opposite the feed side, in a trench (20), to which conveyor belt a transfer track (16) leads from each reel stand (1). A reel core carriage (25) which can travel on said transfer track and on a track section (11) of a moving platform (10) of the reel stand (1) has a chassis (26) and, as a reel core holder, a trough (29) rotatably and tiltably mounted on said chassis. An unloading device for rotating the trough (29) through 90° into an orientation parallel with the conveyor belt (21) and back and for tilting thereof is arranged in a stationary manner at a delivery point (18) at the end of the transfer track (16). After picking up a reel core (17) at the reel stand (1) with trough (29) aligned parallel to the unwinding axes (9) of said stand, the reel core carriage (25) travels to the delivery point (18), where the trough (29) is rotated and, after a cover (22) has been swivelled up, is tilted so that the reel core (17) rolls onto the conveyor belt (21) and is conveyed along the row of reel stands to a reel core container and is disposed of.