This invention provides a compact, fuel-efficient internal combustion engine that can be used to provide rotating shaft output power to a wide variety of mobile and stationary applications. It is based on a two-stroke free-piston gas generator that implements the homogeneous charge compression ignition (HCCI) combustion principle for essentially constant-volume combustion, and it employs a variable piston stroke to maintain a high level of efficiency across a wide range of loads and speeds. A rotary device, which may be of either an aerodynamic or positive displacement type, converts the energetic gas stream to power at a rotating shaft.