The invention relates to an electromechanical friction brake having an electromechanical actuating device including an electric motor and a toothed gear assembly with which a friction brake lining can be pressed against a brake body for braking. Gear wheels of the assembly have sets of helical teeth braced with rotary bearings against the resultant axial forces. Sets of helical teeth have the advantage of better synchronism and of being capable of transmitting greater torque. Moreover, if the friction brake is used as a parking brake, an axial force effected by the set of helical teeth prevents occurrences of microscopic slippage in a locking device with a clamping action and thus prevents unintended automatic release of the locking device.