In an engine in which a lift amount of a valve can be changed continuously, an engine valve operating system including a valve lift-changing mechanism is capable of increasing and decreasing the lift amount of the valve without changing an opening angle for the valve and capable of decreasing a tappet clearance in accordance with a decrease in lift amount of the valve. Thus, it is possible to prevent the ratio of the tappet clearance to the lift amount at a low valve lift from being increased to minimize the influence of the dispersion of the tappet clearance and to reduce the seating speed of the valve at the low valve lift to prevent the generation of a noise. It is also possible to prevent a reduction in performance of the engine at a high valve lift due to the dispersion of the tappet clearance and to decrease the seating noise of the valve at the low valve lift.