Chemical and vibrational nonequilibrium phenomena in steady inviscid flow fields are studied by the analysis of flow past curved boundaries. Possible alternative choices of the state variables to be used are considered. General features of the nonequilibrium flow are studied by examination of the mathematical properties of the nonlinear flow equations. An axisymmetric nonequilibrium flow of air through a supersonic nozzle is analyzed by means of numerical computations. The coupling effects between nonuniformity (across a nozzle section) and nonequilibrium, not taken into account in the quasi-one-dimensional flow approximation, are revealed by the present analysis.