A clamping device (1) for internally centering pipes with respect to one another includes two clamping heads (5, 6), which can be placed into the mutually facing ends of the pipes. The clamping heads each have radially displaceable clamping shoes (7) which are evenly distributed over its external periphery and a drive mechanism (8) for causing the radial displacements of the clamping shoes. Adjusting piston/cylinder devices (10) are provided for adjusting the mutual positions of the clamping heads in the axial direction and a guide element (11) for guiding the clamping heads in the axial direction with respect to one another. Bearings (13) are provided on at least one (5) of the clamping heads and on the guide element (11). The guide element has several guide bodies (12) which are positioned in an eccentric manner in connection with the stability of the clamping heads.