A centering machine for, in particular, optical lenses has two centering spindles. The rotationally drivable centering spindle shafts are axially aligned with respect to a centering axis and constructed at the ends for the mounting of clamping bells. A stroke device axially adjusts one centering spindle shaft relative to the other centering spindle shaft along the centering axis for alignment of the lens between the clamping bells. A clamping device applies to a centering spindle shaft a clamping force clamping the aligned lens. At least one processing unit is movable relative to the centering axis, with a tool for edge processing of the clamped lens. In order to enable an optimized bell clamping process, the stroke device and the clamping device and/or a rotary drive for the axially adjustable centering spindle shaft are arranged coaxially with respect to the centering axis.