Abstract: A fastening system for screening machines and/or setting machines for fastening replaceable screen lining segments and/or replaceable anti-wear elements in or to a screening machine having at least one frame which receives the screen lining segments and/or supports the anti-wear elements. For fastening of a screen lining segment and/or of an anti-wear element at least one adapter is fastened to the frame, the adapter having at least one magnet. The magnet interacts with the frame and/or with at least one ferromagnetic coupling element arranged in a vibration-proof manner in or on the screen lining segment and/or anti-wear element and in this way produces a magnetic connection between the adapter and the frame and/or between the adapter and the screen lining segment and/or anti-wear element. Additionally, a screening machine having such a fastening system.