To obtain a rotary linear synchronous motor which is excellent in characteristics, small and light in weight, and in which the cost reduction can be realized.

The rotary linear synchronous motor has the following characteristics. A moving element 10 is formed as follows. A stator 7 is formed by applying a rotary winding 3 and a linear winding 4 to a stator iron core 2. And at the same time, north-pole magnets 11a are circumferentially and axially arranged on the surface of a cylindrical moving element iron core 5 at one pole interval. And at the same time, south-pole magnets 11b are circumferentially and axially arranged at one pole interval at a position circumferentially and axially displaced by one pole to the north pole magnets 11a. A three-phase AC is impressed to each winding 3, 4. As a result, the moving element 10 can be rotated, linearly moved, and spirally moved.