A system for storing product containers, comprising a plurality of parallel racks, each rack comprising superimposed rows of side-by-side storage positions for product containers, a guide system comprising horizontal longitudinal guides extending between rows of adjacent racks and horizontal transverse guides extending in transverse direction, transversely to the longitudinal guides, as well as junctions at positions where at least one longitudinal guide and at least one transverse guide join one another, the longitudinal guides comprising pairs of parallel longitudinal guide members each having a longitudinal running surface , and the transverse guides comprising pairs of parallel transverse guide members each having a transverse running surface , wherein the longitudinal running surfaces and the transverse running surfaces lie at the same level, the system further comprising trolleys that can move along the guide system, the trolleys each comprising a frame, longitudinal running wheels that roll over the longitudinal running surfaces during movement in the longitudinal direction, transverse running wheels oriented transversely to the longitudinal running wheels, which roll over the transverse running surfaces during movement in the transverse direction, driving means for rotatably driving at least some of the longitudinal running wheels and at least some of the transverse running wheels, vertical adjustment means for moving the longitudinal running wheels and the transverse running wheels up and down relative to each other between a longitudinal position, in which the bottom sides of the longitudinal running wheels are located lower than the bottom sides of the transverse running wheels, so that the trolley is supported on the longitudinal running surfaces with the longitudinal running wheels in the longitudinal position, and a transverse position, in which the bottom sides of the transverse running wheels are located lower than the bottom sides of the longitudinal running wheels, so that the trolley is supported on the transverse running surfaces in the transverse position, and exchange means for transferring a product container to a storage position and taking over a product container from a storage position, wherein at least one longitudinal guide member of each pair of longitudinal guide members comprises at least one longitudinal guide surface and each trolley comprises at least one guide wheel which, upon movement of the trolley in the longitudinal direction, guidingly cooperates with the at least one longitudinal guide surface, characterized in that the upper sides of the longitudinal guide surfaces are located lower than the upper sides of the transverse guide members, at least at the longitudinal positions thereof where the longitudinal running wheels pass the longitudinal guide surfaces in the transverse position of the vertical adjustment means upon movement of the trolley in the transverse direction, and in that the longitudinal guide surfaces comprise recesses at the aforesaid longitudinal positions at the upper sides of the longitudinal guide surfaces, through which, in the transverse position of the vertical adjustment means, lower parts of the longitudinal running wheels move upon movement of the trolley in the transverse direction. <EOS>