Storage device with at least one storage container which comprises a container housing which has an at least essentially rectangular outline and which has a height direction which runs between a lower side and an upper side, a longitudinal direction which runs between a front side and a rear side and is at right angles to the height direction and a transverse direction which is at right angles to the height direction as well as to the longitudinal direction, wherein the container housing comprises a housing lower part which delimits a storage space and which has a base wall and a peripheral wall, said peripheral wall projecting upwards from the edge of the base wall in the height direction and consisting of a front wall, of a rear wall which is distanced with respect to the front wall in the longitudinal direction and of two side walls which are distanced to one another in the transverse direction, wherein an upper end section of the peripheral wall frames an access opening for the storage space, and wherein the container housing further comprises a housing lid, said housing lid being pivotably mounted on the housing lower part in the region of the rear side about a pivot axis running in the transverse direction and by way of a pivoting movement effected relative to the housing lower part being able to be selectively brought into a closure position which closes the access opening or into opening positions which are pivoted upwards to a greater or lesser extent whilst releasing the access opening and the housing lid above one of each side wall of the housing lower part comprising a lateral lid edge section, on whose lower side a downwardly facing lower edge surface is formed, said edge surface in the closure position at least partly covering an upwardly facing upper edge surface of the side wall of the housing lower part which is arranged therebelow, characterised in that the housing lid on the lower side of each of its two lateral lid edge sections comprises a centring strip which projects downwards beyond the lower edge surface and extends in the longitudinal direction of the container housing, said centring strip during a closing pivoting movement of the housing lid, which assumes an open position, immerses from above into the housing lower part next to the adjacent side wall on the inner side facing the storage space and past the upper edge surface of the side wall with an overlapping with respect to the side wall which increases from the rear side to the front side, wherein the housing lid is guidable by the centring strips, which are supportable or supported on the respectively adjacent side wall in the transverse direction, into a closure position which is centred with respect to the housing lower part, characterized in that the width of each centring strip which is measured in the height direction of the container housing gradually reduces from the rear side to the front side of the container housing, in a manner such that its height-related protrusion with respect to the adjacent lower edge surface reduces towards the front side of the container housing and/or that the housing lid on the lower side of the two front lid corner regions, which lie between the two lateral lid edge sections and the front lid edge section which is arranged above the front wall of the housing lower part, each comprises a downwardly projecting centring pin which projects beyond the lower edge surface of the lateral lid edge sections of the housing lid and which in the closure position of the housing lid immerses from above into the housing lower part in a manner supportable or supported with respect to the peripheral wall transversely to the height direction.