Abstract: A time twister cylinder head includes two rotary valves driven by a timing belt coupled to the engine crankshaft by belts and pulleys to describe a desired rate of rotation of the valves with respect to rotation of the crankshaft. Each valve is generally cylindrical with side faces opening in opposite directions to permit coupling with the intake and exhaust manifolds. The common axis of rotation of the valves is slightly offset from the centerline of the air passages so that pressure buildup in the cylinder will be applied off-center on the valves to enhance rotation.