In order to provide an automated parking system for vehicles in which a vehicle which is to be parked is parked on a pallet at a transfer station and the pallet is then transferred by a mechanical device and moved to a storage location, and which, on the one hand, is technically simple, and therefore has little susceptibility to faults, and is cost-effective, and on the other hand can make it possible to use existing storage areas as parking space with minor structural modifications and installations, according to the invention multiple pallets are provided which can be stored at storage locations of the parking system at a raised level with respect to the floor of the building in such a way that a low-floor manoeuvering vehicle can drive under them. Furthermore, at least one robotically controlled, low-floor manoeuvering vehicle is provided for transporting the pallets, said manoeuvering vehicle having an omni-directional drive and being equipped with a preferably hydraulic lifting device in order to lift a pallet which has been driven under.