The problem of predicting the flow properties of a high-temperature gas expanding through a hypersonic nozzle is considered. The equations for the flow of an inviscid adiabatic gas with finite vibrational relaxation and dissociation-recombination rates are integrated analytically where possible to give three integral equations. This set of simultaneous integral equations is then solved by numerical methods. The resulting advantages of this approach are (a) equilibrium need not be assumed at any point and (b) flows in or close to equilibrium can be easily handled. Results are presented for this calculation applied to two nozzles of arc-heated hypersonic wind tunnels and are in substantial agreement with measurements.