Reels of material are transported by being disposed on a first transport carriage which is, in turn, disposed on a second transport carriage. The second transport carriage travels between a reel storage area, that has a plurality of storage spaces, and a reel changer of a web-processing machine. The second transport carriage, together with the first transport carriage and the reel of material that is deposited on the first transport carriage then travels to an offload or unload position of the reel changer.