A high efficiency combined cycle internal combustion and steam engine includes a cylinder with a combustion chamber outward of a piston, a cylinder cap slideably mounted within the piston and a steam expansion chamber inside the piston. The cap can be heated to reduce condensation of steam. Steam remaining when a steam exhaust valve closes can be recompressed prior to admitting the next charge of steam. One valve or a pair of steam inlet valves connected in series act in cooperation to help maximize efficiency. The amount of steam admitted each stroke is regulated by shifting the phase of one steam admission valve of a pair to vary their overlap for determining the steam mass admitted each cycle. Other valves balance steam displacement with the steam generator output to use steam more efficiently.