Abstract: A clamping device for simultaneously machining, internally and/or externally, the two ends of a workpiece, comprising a headstock housing in which a tubular spindle is mounted to rotate, said spindle being internally provided with two annular pistons sliding axially and acting respectively on two collets for clamping the workpiece.The two clamping collets 23, 24 mounted respectively in the two pistons 12, 13 are provided with a cone-shaped portion 21, 22 cooperating with a corresponding cone-shaped portion in the pistons and a cylindrical part 25, 26 centered in the boring of the said pistons, the said collets 23, 24 resting on the side opposite their cylindrical part against the covers 27, 28 fast with the spindle 8 by a cone-shaped face extending radially in order to allow the radial tightening of the collets on the workpiece.The invention is used in lathes with central headstock.