A four-stroke cycle internal-combustion engine having two large- and small-diameter intake valves and two large- and small-diameter exhaust valves in one cylinder and mounted with a valve-operating mechanism on either of the intake valve side and the exhaust valve side. Each valve-operating mechanism comprises a first valve-operating cam of a narrow total valve-opening angle and a low lift, a second valve-operating cam of a wide total valve-opening angle and a high lift, a rocker arm for the small-diameter valve in direct engagement with the first valve-operating cam, a rocker arm for the large-diameter valve, and a connecting means capable of simultaneously operatively connecting the second valve-operating cam with the rocker arm for the small-diameter valve and the rocker arm for the large-diameter valve. In each cylinder at least three spark plugs are mounted. The combustion chamber is formed high on one side and low on the other side.