Abstract: A fixing device for fixing a tool, preferably a turning tool, to a toolholder, includes a shank and at least one cutting part. The toolholder has an insertion opening for accommodating the tool shank. The fixing device includes a clamping element which is stored in such a way that it can partially rotate in the holder around an axis of rotation which is perpendicular to the axis of insertion of the insertion opening. The clamping element also includes a partially cylindrical surface section which is eccentric in relation to the axis of rotation. Furthermore, the shank surface has a partially cylindrical, open-edged recess perpendicular to the shank axis, into which recess the clamp element can be screwed by its partially cylindrical surface section when mounting the tool shank.