The invention relates to a clamping device for clamping at least two components (6, 7) in a radiation-protected machine tool, particularly in a laser welding device (1), comprising—a receptacle (18) for supporting the first component (6), —a clamping head (16) for applying a force to the second component (7) in order to generate clamping pressure at the joint surface (8, 9) between the two components (6, 7), —an inner clamping jaw (11) located within the peripheral beam path (10) of the machine tool, the jaw having a clamping surface (12) for internally clamping the components (6, 7), and—narrow connecting struts (15) for connecting the inner clamping jaw (11) to the external clamping head (16), said connecting struts (15) bridging the passage gap (7) in the clamping head (16) allowing access for the beam path (10) of the machine tool to the components (6, 7).