To suppress the slide when a roller of a roller tappet or a roller rocker arm starts to ascend a cam nose part and reduce the wear of a cam in a structure of an engine valve system.

In a structure of an engine valve system, springing force of a valve spring acts in the direction in which an intake valve or an exhaust valve is closed, the rotary movement of a cam shaft 1 is converted into the reciprocal movement by a roller tappet 2 and is transmitted to one end of a rocker arm, and the movement at the other end of the rocker arm is transmitted to the intake valve or the exhaust valve to open and close the air suction valve or the air exhaust valve. A roller 11 of the roller tappet 2 is pressed lightly toward a cam face of the cam shaft 1 by a spring 22 having smaller springing force than that of the valve spring.