An engine includes at least one cylinder, a first intake valve and a second intake valve associated with the cylinder, to control a flow of intake air from a first intake duct and a second intake duct, respectively. The two intake ducts communicate with a common intake manifold, so as to receive air at the same pressure. During the intake stage, in each cylinder operating cycle, initially an opening and closing movement of only the first intake valve is activated, while the second intake valve remains closed and, subsequently, an opening and closing movement of only said second intake valve is activated, while the first intake valve remains closed. In this way, the two air flows at the same pressure entering the cylinder give rise to a high turbulent kinetic energy, to the advantage of combustion efficiency and reduction of harmful exhaust emissions.