Abstract: A variable valve-timing device for an intake or exhaust valve in a cylinder head of an internal combustion engine operated directly from a camshaft includes a low speed rocker arm mounted on a low speed rocker arm shaft and a high speed rocker arm mounted on a high speed rocker arm shaft. The low speed rocker arm and the high speed rocker arm are interconnected by a pin. A low speed cam is provided on the camshaft corresponding with the low speed rocker arm. A high speed cam is provided on the camshaft corresponding with the high speed rocker arm. The low speed rocker arm shaft and the high speed rocker arm shaft have a common fluted shaft. An outer circular hollow shaft is provided on the common fluted shaft and the low speed rocker arm is mounted on the outer circular hollow shaft.