The transonic flow of a vibrationally relaxing or a chemically reacting gas in a convergent‐divergent nozzle is considered. The procedure used to solve the flow equations is similar to that first used by Hall, and the solution is based on a series expansion in terms of the wall geometry in the transonic region. The nonuniformities of the flow properties across the flow field are taken into consideration. Taulbee and Boraas have already solved such a problem for a frozen flow by a sort of inverse method, in which the governing equations are written with the stream function as an independent variable so as to accomodate the variations in flow properties across the flow field. The problem is solved by a direct method, in which the flow equations are written with generalized coordinates of curvilinear coordinates comprising the streamlines and the system of lines normal to the streamlines, and analytical solutions are obtained for both frozen and equilibrium flows.