Abstract: A two-cycle engine includes a port timing control device for varying a timing of the opening of an exhaust port. The port timing control device include a valve member having an end face curved along a cylinder, the valve member being angularly movable in a direction of the axis of the cylinder between an extended position where the valve member is extended into an exhaust passage with the end face closing an upper portion of the exhaust port and a retracted position where the valve member is retracted from the exhaust passage and fully received in a recess formed in an upper wall of the exhaust passage, with the end case opening the upper end portion of the exhaust port. The end face of the valve member is complementary in shape to an end face of the recess.