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The paper presents a preliminary study on a virtual 2-stroke 3-cylinder 0.9 L DI SI supercharged engine running on Hydrogen (H2), able to meet both high performance targets and ultra-low emissions limits (NOx<20 ppm). Combustion is similar to a conventional 4-stroke H2 DI engine, while the design of the cylinder and the actuation law of both intake and exhaust valves are specifically optimized for the 2-stroke cycle. In comparison to a more conventional 2-stroke loop scavenged engine, with piston-controlled ports, the use of poppet valves enables a more flexible control of the gas exchange process and to maintain the same design of a 4-stroke engine for pistons, cylinders block, crankcase and lubrication system. On the other hand, it is more difficult to avoid the short-circuit of the fresh charge, while permeability of the valves becomes quite critical at high engine speed.