A clamping apparatus may include a stroke-generating disk that is rotatable about a clamping axis and is connected via a first stroke-generating gearing and a second stroke-generating gearing to a pressure disk, which is stationary relative to the rotation of the stroke-generating disk. The first stroke-generating gearing converts a relative rotation of the stroke-generating disk in a first actuating angle range in the clamping direction into a first axial stroke relative to the pressure disk. The second stroke-generating gearing converts a further rotation of the stroke-generating disk following the first actuating angle range in a second actuating angle range into a second axial stroke between the stroke-generating disk and the pressure disk. At least one of the stroke-generating gearings is a tilting pin gearing, with at least one tilting pin supported in the direction of its pin axis between corresponding bearing points on the stroke-generating disk and the pressure disk.