A valve operating system in an internal combustion engine including rollers which are in rolling contact with valve operating cams and rotatably supported by support shafts fixed to rocker arms in a manner such that the support shafts can be easily fixed to the rocker arms. In one embodiment, a rocker arm 25.sub.1 is provided with a fitting bore 37 in which a support shaft 34.sub.1 is fitted and with a press-fit bore 40 leading to an inner surface of the fitting bore 37. A locking groove 43 is provided in an outer surface of the support shaft 34.sub.1 in correspondence to an opening of the press-fit bore 40 into the inner surface of the fitting bore 37, and extends in a direction tangent to a phantom circle C.sub.1 about an axis of the support shaft 34.sub.1. A pin 46 is press-fitted into the press-fit bore 40 and engaged in the locking groove 43.