An internal combustion engine valve operating mechanism wherein there is a low speed cam corresponding to one intake valve or exhaust valve and having a shape designed for low speed operation as well as a high speed cam of a shape designed for high speed operation. A first rocker arm is in sliding contact with the low speed cam and abuts one intake valve or exhaust valve, a second rocker arm is in sliding contact with the high speed cam and a third rocker arm abuts the other intake valve or exhaust valve, with all three rocker arms pivotably supported by a single rocker shaft adjacent to each other. A first piston for connecting the first and second rocker arms is slidably mounted in the first rocker arm and a second piston for connecting the second and third rocker arms is slidably mounted in the second rocker arm extendable and contractable. A third piston is movably mounted in the third rocker arm and urged by a spring in a direction of abutment with the second piston. An annular engaging groove is formed in the outer surface of the first piston, and the first rocker arm is provided with a connecting and disconnection start controlling mechanisms for being engaged with or disengaged from the groove only when the first rocker arm pivots in a valve opening direction. Consequently, the rocker arm connecting and disconnecting operations are performed at the beginning of a valve closing section ensuring the proper completion of the operation.