Abstract: A piston centering system for a free piston machine. The invention uses a centering passageway which is in communication between a work space and a second space which spaces are formed in a housing and are separated by a piston which reciprocates in a cylinder in the housing. The centering passageway has a valve, such as a spool valve formed in the piston and cylinder or a center post, the valve opening in response to the piston being near the center of the opposite limits of its reciprocation. The improvement is the inclusion of a pressure responsive, one way valve interposed in the passageway. The one way valve is oriented to permit the passage of the working gas through the passageway from one space to the other in a direction opposite to a net leakage flow from one space to the other through the annular gap between the piston and cylinder and to prevent substantial flow through the passageway in the reverse direction.