Two-stroke or four-stroke internal combustion engine (M1), operating by admitting a carburated mixture or by admitting fresh air with the direct or indirect injection of fuel, the engine having at least one cylinder (1) defining a variable-volume combustion chamber in which an engine piston (4) coupled by a connecting rod (7) to the wrist pin (8) of a crankshaft (9) executes a reciprocating movement, and a compressor associated with each cylinder in order to supercharge the cylinder with carburated mixture or with fresh air, characterized in that said compressor is a compressor with at least one stage, in the compression chamber (14a, 14b) of which there moves a compressor piston (212) which is coupled to the crankshaft by a link rod (111) articulated to an eccentric (10), said eccentric being mounted on the shaft of said crankshaft.