The invention is directed to an arrangement for fastening permanent magnets to rapidly rotating rotors of electric machines. It is the object of the invention to find a novel possibility for fastening permanent magnets to the rotor of rapidly rotating electric machines which allows the magnets to be fixed so as to be secure against centrifugal forces for high rotating speeds and under confined spatial conditions without a frictionally engaging connection of magnet holders to the rotor. According to the invention, this object is met with a plurality of permanent magnets which are arranged at the outer circumference of the rotor with profile parts which are arranged alternately therebetween in that coaxially extending rotor grooves are introduced in the outer surface of the rotor, the sides of the rotor grooves having contact surfaces which at least partially converge outward with respect to radial direction for contact surfaces of the profile parts which diverge in a conforming manner, and the profile parts are shaped in such a way that they retain the permanent magnets pairwise in a claw-like manner in a positive engagement against radial forces of the rotor rotation. Gaps which inevitably remain at the contact surfaces for reasons of manufacture are filled with a liquid, hardenable medium.