A system for variable actuation of an engine valve of an engine includes a master piston driven by a cam of a camshaft. A slave piston is driven by the master piston by a volume of pressurized fluid. The slave piston causes the engine valve to open, against the action of a spring. A control valve controls a communication between pressurized fluid and an environment at lower pressure, with which a fluid accumulator is in communication. A control unit is programmed for controlling the control valve according to one or more different valve modes. When one of these valve modes is actuated, the control valve opens the communication in advance with respect to the end of the lift cycle of the cam, and not after closing of the engine valve to prevent or reduce a decrease in pressure in the volume of pressurized fluid after closing of the engine valve.