A system for variable actuation of an engine valve of an internal-combustion engine, comprising: - a master piston driven directly or indirectly by a cam of a camshaft of the internal-combustion engine; - a slave piston, which drives said engine valve and is hydraulically driven by said master piston, through a volume of pressurized fluid interposed between the master piston and the slave piston, - said engine valve being recalled by at least one spring into a closed position; - an electrically operated control valve, which controls a communication between said volume of pressurized fluid and an environment at lower pressure, with which a fluid accumulator is in communication, in such a way that: - when the electrically operated control valve keeps said communication closed, the engine valve can be driven by said cam, whereas - when the electrically operated control valve keeps said communication open, fluid can be discharged from the volume of pressurized fluid into the aforesaid environment at lower pressure, so that the engine valve is recalled into its closed position by said spring, and remains unaffected by the movement of said cam; and - an electronic control unit for controlling said electrically operated control valve, - said electronic control unit being programmed for controlling said electrically operated valve in such a way as to actuate the engine valve according to one or more different valve modes, depending upon the operating conditions of the engine, said valve modes including a late-valve-opening mode, in which opening of the engine valve is delayed with respect to the start of the lift cycle determined by the cam profile,, said system being characterized in that said electronic control unit is programmed in such a way that when said late-valve-opening mode is actuated, the control valve opens the aforesaid communication in advance with respect to the end of the lift cycle of the cam, and not after closing of the engine valve, in such a way as to prevent or reduce a decrease in pressure in the volume of pressurized fluid after closing of the engine valve. - a master piston driven directly or indirectly by a cam of a camshaft of the internal-combustion engine; - a slave piston, which drives said engine valve and is hydraulically driven by said master piston, through a volume of pressurized fluid interposed between the master piston and the slave piston, - said engine valve being recalled by at least one spring into a closed position; - an electrically operated control valve, which controls a communication between said volume of pressurized fluid and an environment at lower pressure, with which a fluid accumulator is in communication, - when the electrically operated control valve keeps said communication closed, the engine valve can be driven by said cam, whereas - when the electrically operated control valve keeps said communication open, fluid can be discharged from the volume of pressurized fluid into the aforesaid environment at lower pressure, so that the engine valve is recalled into its closed position by said spring, and remains unaffected by the movement of said cam; and - an electronic control unit for controlling said electrically operated control valve, - said electronic control unit being programmed for controlling said electrically operated valve in such a way as to actuate the engine valve according to one or more different valve modes, depending upon the operating conditions of the engine, said valve modes including a late-valve-opening mode, in which opening of the engine valve is delayed with respect to the start of the lift cycle determined by the cam profile,,