A system for variable actuation of an engine valve of an internal-combustion engine includes a master piston and a slave piston, driven by the master piston. A control valve controls a communication of a volume of a pressurized fluid with a lower pressure environment, which is connected to a fluid accumulator, and an electronic control unit controls the electrically operated control valve. A device for dampening pressure oscillations is connected to the volume of pressurized fluid and includes an additional volume adapted for receiving fluid from the volume of pressurized fluid only when, following upon oscillations of the pressure in the volume of pressurized fluid, the pressure exceeds a maximum threshold value, which is higher than a mean pressure value that is set up in the volume of pressurized fluid when the master piston drives the slave piston in normal operating conditions.