An internal combustion engine includes an electro-hydraulic system for variable actuation of intake valves where each cylinder has two intake valves, associated with two intake conduits. A first conduit is generates within the cylinder a tumble motion of airflow introduced therein, when the intake valve associated thereto is at least partially opened. The second intake conduit generates within the cylinder a swirl motion of airflow introduced therein when the second intake valve is at least partially opened. A controller of controls one or more control valves to open only one of the intake valves of each cylinder in a condition of reduced engine operation, below a predetermined load and/or a predetermined speed of the engine, and to always open both intake valves in the remaining conditions of engine operation. The first intake valve is the only valve to be opened in the reduced engine operation condition.