A combination internal combustion and steam engine (10) includes a cylinder (12) having a piston (14) mounted for reciprocation therein with an internal combustion chamber (34) and a steam chamber (44) in the cylinder (12) adjacent the piston (14) and at least one steam exhaust port (50) positioned to communicate with the steam chamber (44) through the wall (12a) of the cylinder (12) for exhausting steam at a location in the cylinder wall (12a) adjacent to an engine cylinder cap surface (20) that is heated externally to assist in reducing chilling or condensation of steam entering the steam chamber (44) from a boiler (100) fired by waste combustion heat. The invention also permits steam admitted from a steam chest (46) jacketing the cylinder cap (20) to be exhausted from the engine (10) when the steam chamber (44) is in an expanded state whereupon residual steam is then recompressed prior to admitting the next charge of steam with the stream in the steam chamber (44) being heated directly by the combustion chamber (34) as well as by heat from the steam chest (46). An I.C. exhaust (37) powered heater (104) is a part of an I.C. exhaust manifold which functions as an afterburner withsupplemental air injection (146) for promoting combustion of unburned exhaust constituents to superheat steam that is piped through it to the steam chest (46). The invention provides valves for balancing steam engine (10) displacement with boiler (100) output and for cylinder (12) compounding with a boiler (100), heat exchange (106, 108) and control (305) arrangement for efficiently recovering waste heat.