In a storage device (1) and in a storage container (3) which can be loaded into the storage device (1), the storage device (1) has holder means (46) for holding a storage container (3) which are guided so as to be movable between an loading position and an operating position and which are movable out their loading position in a first direction of movement (74) and which are movable into their operating position in a second direction of movement (75) which is oriented transversely to the first direction of movement (74), and the storage container (3) has container-mounted positioning means (15) and the storage device (1) has device-mounted positioning means (156), the cassette-mounted positioning means (15) and the device-mounted positioning means (156) are constructed and arranged in such a manner that during a movement of the holder means (46) from their loading position into their operating position the storage container (3) can be positioned with respect to the device-mounted storage processing means already at the end of the movement in the first direction of movement (74) and during the subsequent movement in the second direction of movement (75) with the aid of the cooperating positioning means (15, 156).