A linear or rotating electric synchronous machine includes a reluctance-secondary part, and a primary part, provided with a coil and permanent magnets. The primary part has teeth, with each tooth surrounded by a coil defining a coil axis. Arranged in each tooth is a permanent magnet which is surrounded by the coil and extends extending in parallel relationship to the coil axis of the coil. The secondary part is constructed for guiding a magnetic field and has teeth which define with the teeth of the primary part an air gap. The permanent magnet defines a magnetization direction in parallel to an air gap plane of the air gap, with the magnetization direction reversing from tooth to tooth.