An oscillating lever arm engine includes rigidly connected opposing pistons moved by a single lever connected to a rotating crankshaft. When applied to a two-cycle internal combustion engine, one piston may function as a pump piston and the second piston as a working piston which delivers power to the crankshaft through a connecting rod. When the pump piston is chosen to be of larger diameter, the volumetric efficiency of drawing in and providing the intake charge to the working piston may be increased. Furthermore, when poppet-type inlet and exhaust valves are used, valve timing may be selected so that the exhaust valve closes prior to the inlet valve closing while the pump piston is supplying an intake charge through a transfer duct to achieve a supercharging effect.