A storage rack having a shelf with storage spaces, arranged over top of each other, for pallets that are horizontally removed sideways. A rack operating device moves the pallets from the spaces, and a station cart forms a lowermost space for a pallet, and can be horizontally moved from the rack on first rails. An upper cart is located above the station cart and forms another one of the spaces to receive a pallet and is horizontally movable on second rails that have a wider track than the first rails and also lead out of the rack. The upper cart has a greater clearance in an area of the station cart which is larger than a length of the pallet, and runs on the second rails, and parts of the upper cart not related to the support structure thereof can be inserted between the vertical rack supports of the rack.