A permanently excited electric machine, comprising a rotor including a shaft having an axis of rotation, a plurality of permanent magnets arranged around the shaft in a circumferential direction for permanent excitation, at least one of the permanent magnets being attached to the shaft, and a flux conducting device for conducting a magnetic flux of the permanent magnets, said flux conducting device having a plurality of separate soft-magnetic flux conducting elements, with each flux conducting element being mounted between two of the permanent magnets and fixed thereto so as to be indirectly held in place on the shaft, at least one of the flux conducting elements having at least one radially outer contact area sized to cover an outer edge of one of the permanent magnets in the radial direction and narrows radially inwardly to a line extending in an axial direction to form a vertex where it contacts the shaft.