Abstract: A brush seal for sealing a gap between two spaces at different pressures on opposite sides of a rotor and a stator. The brush seal is formed as a plurality of bristles and the bristles are mounted in the stator to project radially therefrom, across said gap, to contact the rotor. A clamping ring clamps a stack of the bristles around an annular core in U-shaped fashion with legs of the bristles extending through an annular slot towards the rotor. The clamping ring includes a C-shaped section which clamps the bristles against the core and reverse bend portions at opposite ends of the C-shaped section. The reverse bend portions are axially spaced from one another and form the annular slot through which the legs of the bristles extend.