The invention relates to a hydraulic clamping means, in particular, a clamping nut, for mutual axial clamping of two workpiece sections or machine parts, in particular, a collet and a chuck, comprising an annular housing engaging one workpiece section or machine part, at least one pressure chamber arranged in the housing and filled with hydraulic medium, a pressure screw screwable into this chamber, and an annular pressure area provided in the housing and connected to the pressure chamber, with an annular piston engaging the other workpiece section or machine part axially displaceable in the annular pressure area. To enable direct clamping of two workpiece sections or machine parts in the clamping means itself, the housing and the annular piston comprise clamping surfaces which are directed inwardly and towards one another and each engage one of the workpiece sections or machine parts respectively, and the pressure area, the housing and the annular piston are so constructed and arranged in relation to one another that increasing pressure causes an axial relative displacement of the clamping surfaces towards one another.