Automatic parking system for 10-50 cars on 1 to 5 levels above each other and at least 2 platform rows behind each other. The Level Parker 570 provides spacesaving parking by moving the cars closer together on one or more levels. At each level the cycle movement for transporting the cars takes place by longitudinal and transverse shifting of the platforms. A vertical lift connects the transfer area with the parking levels which can be arranged either above or below ground.