A rack storage system includes first and second storage racks, a rack aisle therebetween, rack guide tracks arranged in pairs in driving planes above each other, a transport vehicle displaceable in the rack aisle, a transport vehicle lifting device with a vertically extending guide frame and a lift frame mounted thereon so as to be adjustable by a lift drive. A receiving device including lift guide tracks positionable relative to the rack guide tracks and by which the vehicle is transportable between the planes is arranged on the lift frame. Vertical first and second guide profiles are connected to the rack guide tracks. First and second lift guide tracks are mounted on the lift frame to be movable parallel to the rack guide tracks by guide devices. First and second coupling devices respectively couple the first and second lift guide tracks to the first and second guide profiles, respectively.