An apparatus controls actual actuation of each of a first and a second valve to the corresponding target actuation. A first computing portion computes the target actuation of the first valve and a target valve overlapping amount according to a engine operational state. A second computing portion computes a requested actuation of the second valve based on the target valve overlapping amount and the target actuation of the first valve. When the requested actuation is out of the permitted range of the second valve actuation, the second computing portion corrects the target actuation of the first valve based on the margin between the requested actuation and a limit of the permitted range. Hence, the engine operational state is maintained in a preferable state.