Abstract: In a chuck for axially clamping two machine parts which are releasable from each other, on the first machine part (1) are provided a hollow centring attachment (3), a contact face (6) surrounding the attachment, and an annular groove (8) formed on the inside of the attachment (3) and comprising a groove flank (9) tapering conically towards the free end of the attachment. The second machine part (2) comprises a holding bore (4) which is adapted to the attachment (3) and which is surrounded by an end face (7) against which the contact face (6) can be pressed. In the second machine part are provided several clamping jaws (10) which are each supported by a first end (10a) against a groove flank (12) in the second machine part (2).