An internal combustion two-strokes engine comprising at least: one cylinder with two pistons inside, facing each other, having an axial reciprocating motion, that make cylindrical cam elements rotate relatively to the pistons and each of said cam elements is coaxial with said cylinder; a frame holding the engine and a straight motor shaft; said internal combustion two-strokes engine is characterized in that: - when said two pistons move towards the ends of the cylinder each of said two pistons pushes towards outside the cylinder a T-rod; - each of said two T-rods comprises a stem parallel to the direction of motion of said two pistons and two arms; - said stem is fixed, on one end, to the piston's back and, on the other end, it is fixed to said two arms that fork in opposite directions and said two arms are terminated with tappets or rollers; - the movement of said stem of said T-rod, referred to the frame of said engine, is purely along its axis without any rotation and said stem slides across a hole obtained in the wall that closes the end of said cylinder to achieve a pre-compression chamber; - said internal combustion two-stroke engine, at each end of each cylinder has a T-rod guidance element which is fixed to the frame of the engine, and said T-rod guidance element binds said arms of the T-rod, so that said T-rod and said relative fixed piston can slide along the axial direction of the cylinder housing said piston, being prevented by said guidance element to spin around said cylinder axis; - said internal combustion two-stroke engine comprises two hollow cylindrical cams associated to each cylinder; - a straight motor shaft is coupled via gear trains, or other similar mechanisms to said two hollow cylindrical cams for the transfer of the motion, and the axis of the straight motor shaft is parallel to the axis of said cylinder. - when said two pistons move towards the ends of the cylinder each of said two pistons pushes towards outside the cylinder a T-rod; - each of said two T-rods comprises a stem parallel to the direction of motion of said two pistons and two arms; - said stem is fixed, on one end, to the piston's back and, on the other end, it is fixed to said two arms that fork in opposite directions and said two arms are terminated with tappets or rollers; - the movement of said stem of said T-rod, referred to the frame of said engine, is purely along its axis without any rotation and said stem slides across a hole obtained in the wall that closes the end of said cylinder to achieve a pre-compression chamber; - said internal combustion two-stroke engine, at each end of each cylinder has a T-rod guidance element which is fixed to the frame of the engine, and said T-rod guidance element binds said arms of the T-rod, so that said T-rod and said relative fixed piston can slide along the axial direction of the cylinder housing said piston, being prevented by said guidance element to spin around said cylinder axis; - said internal combustion two-stroke engine comprises two hollow cylindrical cams associated to each cylinder; - a straight motor shaft is coupled via gear trains, or other similar mechanisms to said two hollow cylindrical cams for the transfer of the motion, and the axis of the straight motor shaft is parallel to the axis of said cylinder.