The subject to be discussed is that in which many elementary chemical reactions occur simultaneously in a gas undergoing laminar, steady, adiabatic flow through a supersonic expanzion nozzle. Some general comments on the techniques involved in the numerical analysis of this type of non-equilibrium flow with a high-speed digital computer will be given but the emphasis throughout is on the chemical kinetic aspects of the problem. All internal degrees of freedom of the molecules are assumed to be in equilibium with the local translational temperature everywhere. The flow is taken to be one dimensional in the usual fluid dynamic sense. The interaction between chemical and fluid dynamic variables is illustrated by actual results on two types of mixtures. The first is characteristic of many ordinary solid or liquid rocket propellant exhaust gases and contains the species H 2 , H 2 O, CO, CO 2 , H, and OH. The reasons for assuming that these take part in four elementary (reversible) reactions of importance are given. The second example considers a mixture containing the active species H 2 , H 2 O, O 2 , H, OH and O such as would be involved in a hydrogen-flueled ramjet, where eight elementary reactions are used. The relative significance of two-body and three-body reactions in influencing the gas composition of other flow variables is discussed. Some indication of the sensitivity of the results to the magnitudes assumed for the rate constants will be given. The degree of utility and validity of various popular approximations in this field is assessed, and some practical implications pointed out.