A supercharged diesel engine is equipped with an electronically controlled hydraulic system for variable actuation of the intake valves of the engine. The cam that controls each intake valve has an additional lobe for causing an additional opening of the intake valve, during the expansion and exhaust strokes, so as to provide an exhaust-gas recirculation directly inside the engine. The aforesaid additional lobe has its descending stretch radiused to the main lobe with a stretch corresponding to a non-zero lift of the valve in such a way that the profile of the lift of the valve has a portion corresponding to a substantially non-zero value of the lift that radiuses the descending stretch of the profile of the additional lift to the ascending stretch of the profile of the main lift.