A variable actuation system for actuating an engine valve of an internal combustion engine, comprising: - a movable member in form of a master piston , controlled, directly or indirectly, by a cam of a camshaft of the internal combustion engine, and connected hydraulically to the engine valve , - a slave piston , which actuates said engine valve and which is hydraulically controlled by said master piston , by means of a volume of pressurized fluid (C) interposed between the master piston and the slave piston , - at least one return spring biassing the engine valve to a closed position, - an electrically-actuated control valve , which controls the communication between said volume of pressurized fluid (C) and an environment at a lower pressure connected to a fluid accumulator , in such a way that: - when the electrically-actuated control valve keeps said communication closed, the engine valve can be actuated by said cam , while - when the electrically-actuated control valve keeps said communication open, fluid may discharge from the volume of pressurized fluid (C) into the aforesaid lower pressure environment , so that the engine valve remains insensitive to the movement of said cam , - an electronic control circuit to control said electrically-actuated control valve , - said electronic control circuit being programmed to control said electrically-actuated valve in such a way as to actuate the engine valve according to one or more different valve modes, depending on the operating conditions of the engine, said system being characterized in that it comprises an auxiliary device (S; 801; 900) for applying an additional force to the engine valve , tending to maintain the engine valve in its closed position, said auxiliary device (S; 801; 900) being configured or controlled in such a way that the total force tending to keep the engine valve in its closed position varies during each rotation cycle of the actuating cam of the engine valve , said total force being higher at least in the part of the rotation cycle of the cam in which the engine valve must remain in its closed position, that is both in the part of the actuating cam rotation cycle, in which the cam cannot cause movement of the master piston, and also in all conditions in which the variable actuating system excludes the coupling between the cam and engine valve by discharging the volume of pressurized fluid, said force being instead reduced at least in a part of the rotation cycle of the cam in which the engine valve is not in its closed position. - a movable member in form of a master piston , controlled, directly or indirectly, by a cam of a camshaft of the internal combustion engine, and connected hydraulically to the engine valve , - a slave piston , which actuates said engine valve and which is hydraulically controlled by said master piston , by means of a volume of pressurized fluid (C) interposed between the master piston and the slave piston , - at least one return spring biassing the engine valve to a closed position, - an electrically-actuated control valve , which controls the communication between said volume of pressurized fluid (C) and an environment at a lower pressure connected to a fluid accumulator , - when the electrically-actuated control valve keeps said communication closed, the engine valve can be actuated by said cam , while - when the electrically-actuated control valve keeps said communication open, fluid may discharge from the volume of pressurized fluid (C) into the aforesaid lower pressure environment , so that the engine valve remains insensitive to the movement of said cam , - an electronic control circuit to control said electrically-actuated control valve , - said electronic control circuit being programmed to control said electrically-actuated valve in such a way as to actuate the engine valve according to one or more different valve modes, depending on the operating conditions of the engine, <EOS>