The invention relates to a transport vehicle (7) for storing unit loads in a storage rack (1) and removing unit loads from a storage rack. The transport vehicle comprises a base frame (27), running wheels (29) which rest on a first guide (36) in a rollable manner, the first guide extending parallel with the longitudinal direction of the storage rack and in a first guide plane extending parallel with a driving plane, and a guide unit (31; 60; 62; 74; 86) which is mounted to the base frame via a bearing device (46; 61; 63; 75; 87) and has guide wheels (49) which rest on a second guide (47; 88) and are rollable in guide sections (48), the second guide extending parallel with the longitudinal direction of the storage rack and in a second guide plane intersecting the driving plane in order to move the transport vehicle in a guided manner. The bearing device comprises an elastic compensating element (53; 54; 67, 68; 79, 80) which is arranged in such a way that one of the guide wheels is movable relative to the base frame. The invention further relates to a method for storing different unit loads on differently classified storage spaces.