A system for operating an internal combustion engine including an intake valve and an exhaust valve, the system including an exhaust valve gear for the exhaust valve which incorporates an exhaust variable valve timing mechanism. The system also includes an intake valve gear for the intake valve which incorporates an intake variable valve timing mechanism. A control unit operates responsive to a low-speed/low-load operating range of the engine and a low-speed/high-load operating range of the engine to condition the exhaust variable valve timing mechanism for providing advanced opening and closing timings of the exhaust valve to cause a reduced valve overlap between the intake and exhaust valves, and at the same time condition the intake variable valve timing mechanism for decreasing an opening duration of the intake valve to provide a retarded opening timing thereof after a top dead center and an advanced closing timing thereof. The control unit operates responsive to a low-speed/medium-load operating range of the engine to condition the exhaust variable valve timing mechanism for providing retarded opening and closing timings of the exhaust valve to cause an increased valve overlap between the intake and exhaust valves, and at the same time condition the intake variable valve timing mechanism for increasing the opening duration of the intake valve to provide an advanced opening timing thereof before the top dead center and a retarded closing timing thereof.