An internal-combustion engine with two intake valves for each cylinder is provided with a system for variable actuation of the intake valves, including a single solenoid valve for each cylinder that controls communication of a pressurized-fluid chamber of the system with an exhaust channel. The solenoid valve is a three-way, three-position solenoid valve, including an inlet permanently communicating with the pressurized-fluid chamber and with the hydraulic actuator of an intake valve, and two outlets communicating, respectively, with the actuator of the other intake valve and with the exhaust channel. The solenoid valve has a first position, in which the inlet communicates with both of the outlets, a second position, in which the inlet communicates only with the aforementioned outlet connected to the actuator of an intake valve and does not communicate, instead, with the outlet connected to the exhaust channel, and a third position, in which the inlet does not communicate with any of the two outlets.