When gases flow at high velocity, the rates of internal processes may not be fast enough to maintain thermodynamic equilibrium. By defining quasi‐equilibrium in flow as the condition in which the temperature, pressure, density, and velocity deviate by less than a fixed, small percentage from what they would be if the flowing gas could actually be in thermodynamic equilibrium, criteria are derived for determining whether quasi‐equilibrium is a stable condition in the flow. By use of excitation of molecular vibration as an example, the general properties of criteria curves are discussed and interpreted. A discussion is given of how to use these results to determine definitely whether a flow is or is not in thermodynamic equilibrium. Applications to dissociating gases, to mixtures, and to the phenomenon of ``choking'' in a Laval nozzle are given special consideration. For cases when application of the criteria predict nonequilibrium, equations are provided in a form useful for numerical forward integration along streamlines.