A clamping fixture for detachably fixing a tool to a driven spindle and comprising a flange for applying a clamping force to the tool and axially displaceable relative the driven spindle and coupled to the driven spindle for transmitting a torque thereto, a supporting element for securing the flange against axial displacement relative to the spindle to prevent the flanges from applying a damping force to the tool, the supporting element comprising an annular nut member displaceably mounted on the spindle adjacent an end of the flange which is remote from the tool, and having a right-hand coarse thread to be screwed onto the threaded portion with an external coarse thread of the spindle, a torsion spring for coupling the annular nut member to the flange, and a locking device for preventing rotation of the annular nut member upon actuation of the locking device.