The invention relates to a self-cooling backheating movable cylinder fuel-air engine and Stirling engine. The engine comprises a crankshaft, a connecting rod component, a pipeline, a hydraulic tappet, a cylinder head, a piston ring, a piston, a movable cylinder, a middle cylinder, an outer cylinder, a sensor, a valve component, an electric control hydraulic valve, a nozzle, a high-pressure electronic pump, an electric flow valve, an exhaust gas recirculation system, a booster, a power machine, a valve, a turbine, a compressor and a cooler, and is characterized in that: two internal combustion engines, namely a heat release engine and a heat absorption engine consist of the movable cylinder, the piston fixed in the movable cylinder and the middle cylinder outside the movable cylinder; the engine has a compact structure and is convenient to assemble and maintain; the heat absorption engine absorbs heat from the periphery of the heat release engine and an exhaust gas regenerator to do work and reduce temperature, so that the cylinder temperature is appropriate; a cylinder cooling system is saved; the heat is prevented from being taken away by cooling, exhaust heat is recovered outside, the heat is absorbed inside for doing work and self-cooling, most of consumed heat is recycled, and the heat efficiency of the whole engine is obviously improved; and the engine also can be taken as an air engine, is energy-saving, environmental-friendly, high-efficiency and ideal and can be widely applied to various fields.