An internal combustion engine (1) has a positive displacement supercharger (8) which can be used with particular advantage in an underpumping two stroke engine which is in the form of a valved diaphragm which reciprocates in a housing to deliver positive pulses of air. The internal combustion engine (1) also has an oiling system which comprises injecting oil between the piston (4) and cylinder walls (2) at discrete time intervals and any excess oil is removed through galleries in the piston (4), con rod (5) and main shaft (6) preferably by a vacuum exerted on the galleries. Various other innovative features include a two part exhaust valve (9), generation of the vacuum by a positive displacement supercharger, a two-part cylinder head (3), use of inserts on moving parts to increase the efficiency of an underpumping engine and a specially constructed flywheel (11).