A valve-operating system for an internal combustion engine includes cam followers which have cam abutment portions abutting against valve-operating cams provided on a camshaft and which are swingably carried in an engine body and operatively connected to engine valves biased in a closing direction by a valve spring. The cam followers are biased in a direction of abutment of the cam abutment portions against the valve-operating cams by a resilient biasing means different from the valve spring. A resilient biasing means includes a pull rod connected at one end thereof to the cam follower, and a compression coil spring interposed between the other end of the pull rod and the engine body to pull the pull rod to bias the cam follower in a direction of abutment of the cam abutment portion against the valve-operating cam. Thus, the resilient biasing means is constructed to be compact, leading to an increase in degree of freedom of the design of the structure of the valve-operating system.