Abstract: The present invention is a compound internal-combustion hot-gas engine comprising a housing wherein there are internal-combustion means and hot-gas means which are coupled mechanically by a single crankshaft, coupled thermally by a thermal energy recuperator-transfer unit, and also coupled thermally by a circulating liquid cooling system. The compound engine has a plurality of cylinders and reciprocating pistons. The cylinders are grouped in either a linear, vee, or flat planar geometrical distribution. Preferred embodiments include a compound engine possessing three cylinders and progress continuously to engines possessing an arbitrarily large number of cylinders. The compound engine is particularly useful as a prime mover for automobiles, trucks, busses, locomotives, maritime vessels, farm implements, and stationary power sources, but is not limited to such uses.