Disclosed is a clamping device of a balancing machine for coaxially clamping a toolholder on a spindle rotary about an axis of rotation (3), in which the coupling shank (8) is supported in the receiving socket only on discrete supports (11-15) which are spaced from each other circumferentially and lie in three relatively spaced engagement planes (E1, E2, E3) intersecting the axis of rotation (3). Four rigid discrete supports (11-14) are arranged in pairs in the first (E1) and the second (E2) engagement plane and combine to form a rigid support in a first radial direction. Formed in the third engagement plane (E3) lying between the first and the second engagement plane is a fifth discrete support (15) which effects a supporting function in a second radial direction opposite the first radial direction.