A valve operating system for internal combustion engines, comprising a rocker arm support member provided with an oil passage in an inner portion thereof, a cam shaft provided with a valve operating cam thereon, a roller shaft provided on an outer circumference thereof with a roller contacting the valve operating cam via a needle bearing while rolling, and a rocker arm provided with first and second support wall portions mutually spaced each other and opposed to each other, the first support wall portion having a bottomed portion-carrying engagement bore, the roller shaft being inserted in the engagement bore, the rocker arm being provided in an inner portion thereof with an oil supply passage for supplying a lubricating oil from the rocker arm support member to the engagement bore, wherein the improvement lies in that a clearance is provided between the end portion of the roller shaft which is most distant from the rocker arm support member and the bottomed portion.