An improved control device for intake and/or exhaust valves of an internal combustion engine includes a small circumference portion defined in a drive shaft at a location corresponding to that of an annular member which is eccentrically displaced for changing a rotational phase of the cams. According to this a degree of displacement of the annular member may be increased and control the cams, and thereby the engine valves, may be enhanced. Further, the cam lobe of each cam is formed such that side portions thereof are asymmetrical with respect to a center line of the cam for favorably affecting valve opening and closing timings. In addition, an improved lubricating arrangement for enhancing smooth operation and improved engine performance.