An electromagnetic engine has inner and outer rotors having magnets of opposite polarity mounted thereon. Output is taken from the inner rotor, which is free to unidirectionally rotate. The outer rotor is caused to oscillate, the force of magnetic repulsion between the magnetic fields of the inner and outer rotors driving rotation of the inner rotor. The outer rotor may be held stationary by solenoids and holding gears when the inner and outer magnetic fields are closely adjacent in order to maximize the force of repulsion. The timing of the oscillation and pausing of the outer rotor may be controlled by EPROM circuitry and a timing sensor mounted on the output shaft or gear. Alternatively output is taken from the outer rotor, which is free to unidirectionally rotate while inner rotor is caused to oscillate, the magnetic forces between the inner and outer rotors driving rotation of the outer rotor.