A phase and stroke control apparatus for the pistons of a Stirling engine includes a ring on the end of each piston rod in which a pair of eccentrics is arranged in series, torque transmitting relationship. The outer eccentric is rotatably mounted in the ring and is rotated by the orbiting ring; the inner eccentric is mounted on an output shaft. The two eccentrics are mounted for rotation together within the ring during normal operation. A device is provided for rotating one eccentric with respect to another to change the effective eccentricity of the pair of eccentrics. A separately controlled phase adjustment is provided to null the phase change introduced by the change in the orientation of the outer eccentric, and also to enable the phase of the pistons to be changed independently of the stroke change.