Clamping device (21) for clamping an optical disc on a turntable comprises a disc-pressure means (23), a support (5) for the disc-pressure means, which support is movable between an operating position and a rest position, and a permanent-magnet system comprising a first axially magnetized annular magnet (31) and a second axially magnetized magnet (29) secured to the support and to the disc-operating means respectively. In the operating position of the support the disc-pressure means is pressed against the disc on the turntable by magnetic force and the disc-pressure means is freely rotatable relative to the support. The permanent magnets are positioned coaxially relative to each other, a radial air gap (33) being formed between the first magnet (31) and the second magnet (29) in the operating position of the support.