Atmospheric flight of space vehicles during take-off and re-entry from space (either from a planetary mission or from any Earth orbit) normally takes place with free-stream Mach numbers up to approximately 30. For such high flight Mach numbers and low air densities the gases around the space vehicles are in thermodynamic non-equilibrium. The related phenomena are: The followingReal gas flowThermodynamic state chemical reactionsThermodynamic state dissoziationsThermodynamic state recombinationsThermodynamic state excitation of molecular vibrationsThermodynamic state electron modesThermodynamic state ionization three sections describe the thermodynamic non-equilibrium due to chemical reactions, excitation of molecular vibrations as well as ionization. Section 9.4 addresses gases in thermodynamic equilibrium. The species continuity equations in arbitrary coordinates is given in Sect. 9.5.