The storage device includes slider members, each having a resilient clasp element for receiving and holding a recording medium housing. Each of the slider members is spring-loaded and slidable between a storage position in the storage device housing and an unloading position contained completely within the housing. In the unloading position a recording medium housing held by the slider member projects from a housing opening in the storage device housing so that it can be removed from the slider member but the slider member need not be pushed back. The storage device has a locking device for each slider member including a resilient blade attached to the storage device housing at one end and having a latching element at the other end so that, when a recording medium housing is put into a housing opening and received by a slider member in the unloading position, it can be pushed into the housing and secured in the storage position. An unlocking device including a push button mounted on the housing next to each housing opening is provided so the slider member can be released from the storage position to slide into the unloading position simply and reliably.