This motor is of the type comprising a case having a cylindrical upper part in which a piston is slidably mounted and a lower part in which a crankshaft connected to the piston is disposed. The case further comprises on one hand, an intake port and an exhaust port which open onto the upper part of the case, the input port being disposed below the exhaust port, and, on the other hand, at least one transfer conduit interconnecting the two parts of the case.The motor comprises a supply circuit for non-carburetted fresh gases which is connected to at least one port of the upper part of the case, the upper edge of this at least one port being disposed below the upper edge of the exhaust port.The motor is applicable in particular to motorcycles.