The sterile cover system for sterilely covering a medical technical robot arm with a connecting element, having a receiving bore with an inner wall, for endoscopic devices, is provided with a sack-shaped drape for enclosing the connecting element. The drape comprises a film tube which is adapted to the receiving bore for covering the inner wall, and a guiding element which is removably attached to a first end of the film tube, adapted to the receiving bore and extends into the film tube in an initial state of the sterile cover system. The film tube can be inserted into and guided through the receiving bore by means of the guiding element such that a surface of the film tube, facing inward in an initial state of the sterile cover system, faces the inner wall of the receiving bore in a state in which the film tube is guided through the receiving bore.