A method for operating a reciprocating piston-type internal combustion engine selectively in two-stroke, four-stroke, and six-stroke mode includes: providing transfer valves, transfer passage means between piston cylinders, selectively controlling the actuation and timing of the intake, exhaust and transfer valves, and alternatively operating the intake and exhaust valves for each piston cylinder in overlapping sequence during each crankshaft revolution to provide two-stroke operation, operating the intake and exhaust valves in sequence during each second crankshaft revolution to provide four-stroke operation, operating the intake, exhaust, and transfer valves sequentially to cause a secondary expansion stroke in an adjacent piston cylinder to provide six-stroke operation of the engine.