Device for clamping a workpiece holder on a collect chuck that can be fixed to a machine tool, having clamping elements distributed around the circumference of the collet chuck. The clamping elements can be adjusted radially to the axis of the collect chuck from a release to a clamping position and can be pressed against a circumferential surface of the workpiece holder positioned relative to the collet chuck in the clamping position. The clamping elements are designed as rollers having axes aligned nearly tangentially to the collet chuck circumference. A determinable surface pressure thus results in the clamping position as the rollers mutually contact the workpiece holder, a clamping mandrel of the collet chuck, and the collect chuck part. The surface pressure is thereby reduced and the collet chuck can also be used in the range of greater tensile forces.