The invention relates to an electric synchronous machine. There is a need for a dual rotor electric synchronous machine which has a mechanism for adjusting the rotor relative angular displacement while the machine is running in order to reduce back EMF. There is a need for such an adjusting mechanism which can carry high torque loads. An electric synchronous machine is provided with a housing, first and second shafts rotatably supported in the housing, each with a corresponding rotor fixed thereon, both having permanent magnet field poles. Each rotor is surrounded by a corresponding annular stator, and stator coils are wound through both stators. A planetary transmission is coupled between the first and second shafts and operable during rotation of the first and second shafts to adjust an angular orientation of the second shaft with respect to the first shaft.