A method and apparatus in which a stator (11) and a rotor (12) define a primary air gap (20) for receiving AC flux and at least one source (23, 40), and preferably two sources (23, 24, 40) of DC excitation are positioned for inducing DC flux at opposite ends of the rotor (12). Portions of PM material (17, 17a) are provided as boundaries separating PM rotor pole portions from each other and from reluctance poles. The PM poles (18) and the reluctance poles (19) can be formed with poles of one polarity having enlarged flux paths in relation to flux paths for pole portions of an opposite polarity, the enlarged flux paths communicating with a core of the rotor (12) so as to increase reluctance torque produced by the electric machine. Reluctance torque is increased by providing asymmetrical pole faces. The DC excitation can also use asymmetric poles and asymmetric excitation sources. Several embodiments are disclosed with additional variations.