A stepped-piston, internal-combustion engine includes at least one cylinder, each cylinder having a working part (12) of lesser diameter defined by a cylindrical wall (21) and a pumping part (13) of greater diameter, a piston slidable in each cylinder, a receiver (25) which is partly delimited by the cylindrical wall (21) of the working part of each cylinder and which extends at least partly around each working part, working inlet ports (23) in the cylindrical wall and extending between the working part of the cylinder and the receiver and valve means (30, 39) to control the entry of charge into the pumping part (13) of each cylinder and the transfer of charge from said pumping part (13) to the receiver (25) is controlled by the uncovering of the working inlet ports (23) by the working part of the piston.