In order to keep the load on the cables in a cable storage device as light as possible during the process of storing, and furthermore in order to keep the release of the cables as simple as possible, a cable storage device is provided in which at least on one side of the storage device a shoulder of a block is provided, which during storage is pushed down by the cable gripper, and as a result of this during storage the cable or cable end is practically not exposed to any transverse or longitudinal load. In this arrangement the block with the shoulder or shoulders is pushed upward by a spring and in this way ensures reliable clamping action in the storage device.