A valve operating system for an internal combustion engine including a main valve lifter, a subsidiary valve lifter, a low-speed cam operating the main valve lifter, a high-speed cam operating the subsidiary valve lifter, a connecting device switched over between a non-connecting state in which the valve lifters are disconnected from each other, and a connecting state in which the valve lifters are connected to each other, a valve spring for biasing the valve in a closing direction, a lifter spring for biasing the subsidiary valve lifter toward the cam; thus, in a low-speed mode, that is non-connected states, an influence of a load of the lifter spring on the valve can be prevented, and in a high-speed mode, that is connected states, a sum total of loads of the valve spring and the lifter spring cap be applied to both of the valve lifters to improve the closing responsiveness of the valve.