Provided is a variable valve operating apparatus for an internal combustion engine, which can switch, based on an actuation of a single actuator, operating characteristics of valves for a plurality of cylinders collectively and smoothly using a rigid member, while suppressing an increase in wear of a guide rail and reducing the number of delay mechanisms.A changeover mechanism to switch operating characteristics of valves for each cylinder of first and second cylinder groups is provided. The changeover mechanism includes link shafts as a rigid member which is displaced when being engaged with a helical guide rail as a result of the actuation of an electromagnetic solenoid. The changeover mechanism includes a delay mechanism, which delays the displacement of the second link shaft in a cylinder in which the valves are lifting when the electromagnetic solenoid is actuated, at some point in the link shafts between the first cylinder group and the second cylinder group.