An internal combustion engine comprises a cylinder of stepped configuration having a working portion (21) and a pumping portion (22) and a piston of stepped configuration having a working portion (31) and a pumping portion (32), the working (21, 31) and pumping portions (22, 32) respectively co-operating to define a combustion chamber (35) and a pumping chamber (37) each of which varies in volume upon reciprocation of the piston in the cylinder. Air is admitted to the pumping chamber (37) through a duct (43) from where, on volume reduction thereof, it passes via a plurality of passages (49) and a one-way valve (50) into a transfer chamber (47). On volume expansion of the combustion chamber (35), air in chamber (47) is discharged therefrom via a plurality of passages (55), common discharge port (57) and valve (59) to scavenge the combustion chamber (35) and provide combustion air. The valve (59) may be self-acting or operated by a crankshat controlled push-rod. A delivery pump (63) operated pneumatically under the influence of the pumping chamber (37) to deliver fuel or a combustible mixture to inlet passage (76) is also disclosed.