Rotary valve system for controlling communication with a port in an internal combustion engine which, in one disclosed embodiment, has a crankshaft, compression and expansion pistons connected to the crankshaft for reciprocating movement within compression and expansion chambers, a combustion chamber in which air from the compression chamber is combined with fuel and burned to produce an increased gas volume. The valve system has an outer valve member which is rotatively mounted in a bore and has an opening which moves into and out of communication with the port as the outer valve member rotates, an inner valve member rotatably mounted within the outer valve member with an opening at least partly overlapping the opening in the outer valve member, a flange extending along one edge of the opening in the inner valve member and through the opening in the outer valve member for sealing engagement with the wall of the bore, and means for effecting rotation of the valve members to change the degree of overlap between the openings and thereby control the timing and duration of communication between the openings and the port.