An internal combustion engine for motor-vehicles, includes a system for variable actuation of the intake valves of the engine having a solenoid valve controllable between a closed condition and an open condition wherein it places a pressurized fluid chamber in communication with an exhaust chamber, with the aim of decoupling the intake valve from the respective tappet and causing the quick closing of the intake valve due to the respective return spring. The solenoid valve has a valve element with a cylindrical body having a first conical surface portion and a second conical surface portion. The conical surface portions are defined by the axially opposite ends of a circumferential groove formed on the valve element. The first conical surface portion cooperates with the valve seat. The other conical surface portion has an outer diameter substantially identical to the diameter of the annular edge defining the valve seat.