A forced opening and closing valve operating system for changing the operating characteristics of an engine valve according to low speed running conditions and high speed running conditions of the engine, includes a low-speed free rocker arm that swings by following a low speed valve-opening cam and a low speed valve-closing cam, a high-speed free rocker arm that swings by following a high speed valve-opening cam and a high speed valve-closing cam, and a valve operating rocker arm that is sandwiched between the low-speed and high-speed free rocker arms and is connected to an engine valve for driving the engine valve in both valve-opening and valve-closing directions. The rocker arms are swingably supported on a rocker shaft. Connection switching means switches alternatively connecting the valve operating rocker arm to the low-speed and high-speed free rocker arms. Thus, the valve operating system is compact, and noise generation is prevented.