A clamping device for fastening a member, such as a hollow shaft or hub, to a shaft includes a ring element which is provided with a cylindrical inner surface and has an end side which includes a plurality of axial threaded bores. The ring element is attached to one end of the member and axially fixed on the member by a support shoulder of the member and a securing ring fastened to the member. A clamping element has an end-side flange which is provided with a plurality of axial passage openings for receiving clamping screws. The clamping element has a portion provided with an outer taper and arranged radially between the shaft and an inner taper of the member, with the clamping element being threadably engaged to the ring element.