For hysteresis couplings or brakes, a multi-pole magnetized magnet faces a disc of hysteresis material (hysteresis material is a non-magnetized permanent magnet material with high residual induction and low coercive field strength). The turning or braking torque depends on the dimensioning, the magnetic material, the number of poles and the air gap. The turning or braking torque is largely independent of the relative speed and is fully available even at very low relative speed. If necessary the torque or brake moment can be slightly adjusted by axial displacement that means by changing the air gap. These couplings / brakes are suitable for high speeds.