The two-cycle internal combustion engine includes an engine block having a cylindrical wall defining a cylinder having a head end, a piston mounted for reciprocative movement in the cylinder, and a passage in the engine block, such as an exhaust passage, a transfer passage, or a crankcase fuel intake passage, terminating at the cylinder wall in a port, such as an exhaust port, a transfer port or a piston-controlled, crankcase fuel intake port, having upper and lower edges. A valve mounted in the passage for movement relative to the port is operable to selectively vary the effective distance of one of the port edges from the cylinder head end and thereby provide the capability of varying the timing of the port opening and/or closing as required to obtain optimum engine performance at different operating conditions.