The actuating arrangement for a tool clamping device (1) has a clamping bar (3) which is axially displaceable in a clamping direction in a machine tool spindle (2) under the effect of a spring arrangement (11) and a firsst wedge transmission assembly (9) which is operable between the spindle and the clamping bar, with freely movable balls which bear respectively against three cone surfaces. They are disposed on a clamping sleeve (13) which is axially displaceable on the clamping bar, on a clamping ring (14) connected to the clamping bar (3), and on a support ring (15) which is arranged stationarily with respect to the spindle. The spring arrangement (11) acts by way of a pressure sleeve (12) which is axially displaceable on the clamping bar. Disposed between the pressure sleeve (12) and the clamping sleeve (13) is a second wedge transmission assembly (10) with freely movable balls which respectively bear against two cone surfaces which are inclined in mutually opposite relationship on the mutually facing ends of the two sleeves (12, 13) and successively against two further cone surfaces which are inclined in opposite relationship on the support ring (15). In the release stroke movement in opposite relationship to the clamping direction a piston-cylinder unit (7, 8) initially acts on the clamping sleeve (13) and then also on an annular shoulder (3a) of the clamping bar (FIG. 1).