A Stirling engine was invented 200 years ago. Its author was ahead of its time. Only in the 50s of the last century its satisfactorily working samples were manufactured by Phillips. A cryogenic gas machine (CGM) working on the reverse Stirling cycle was developed and experimentally investigated at the same time. Key indicators of CGM with discontinuous and harmonic character of piston movement are described in the paper. It is shown that in a real Stirling machine with losses from internal and external irreversibility there can be achieved optimal cooling temperature at which the degree of thermodynamic perfection becomes the maximum. Results of arrangement of various CGMs, including Stirling, working with the unsteady flow of the working fluid are considered. Place of the Stirling cryogenic machine family made in the considered systematization, which uses only the general thermodynamic features, is determined.