Procedures are developed for determining the inviscid core and boundary layer development in diverging nozzles with high enthalpy reservoir conditions in which the gas composition has been displaced from equilibrium by chemical relaxation. A finite difference procedure, based on the method of characteristics, is used for the inviscid flow with finite rate chemical reactions. Laminar boundary layer profiles, based on local similarity, are obtained by integrating the coupled boundary layer and chemical reaction equations outward from the nozzle wall. Free stream boundary conditions on the chemical specie concentrations and the thermodynamic variables are satisfied by iterating o the unknow concentrations and derivatives at the wall. Numerical calculations are presented for the AEDC, VKF low density tunnel and the Convair hypersonic shock tunnel. Effects of chemical reactions in the boundary layer are restricted to the region in which the core flow has not yet frozen and in which the boundary layer is thin. When the boundary layer is thick enough to influence the core expansion, gas phase reactions are frozen. (Author).