An internal-combustion engine with two intake valves (7A, 7B) for each cylinder is provided with a system for variable actuation of the intake valves, comprising a single solenoid valve for each cylinder that controls communication of the pressurized-fluid chamber (C) of the system with an exhaust channel (23). The solenoid valve is a three-way, three-position solenoid valve, comprising an inlet (i) permanently communicating with the pressurized-fluid chamber and with the hydraulic actuator of an intake valve (7B), and two outlets (u1, u2) communicating, respectively, with the actuator of the other intake valve (7A) and with said exhaust channel. The solenoid valve has a first position (P1), in which the inlet communicates with both of the outlets, a second position (P2), in which the inlet communicates only with the aforesaid outlet (u1) connected to the actuator of an intake valve (7A) and does not communicate, instead, with the outlet (u2) connected to the exhaust channel (23), and a third position (P3), in which the inlet (i) does not communicate with any of the two outlets (u1, u2). There is envisaged an operating mode in which the solenoid valve is brought into said second position (P2) in an active phase of the tappet in which the tappet (15) tends to bring about opening of the second intake valve (7A) so that said second intake valve (7A) opens. The solenoid valve (24) is then brought into said third position (P3) when the aforesaid active phase of the tappet is still in progress, so that the hydraulic actuator of the second intake valve (7A) remains isolated and the second intake valve (7A) remains blocked in the open position in which it is, even when the tappet (15) no longer tends to keep it open.
