Abstract: The numerical simulation of chemically reacting flows in the nozzle is accomplished by a time-dependent technique using semiimplicit scheme.A second-order implicit difference approximation is applied to the time derivatives in governing equations and a noncentered difference approximation is explicitly employed to the spatial derivatives.The numerical instability caused by the stiffness of chemical relaxation equations is succesfully depressed by the above measure.The results obtained from numerical simulation of one-dimensional and axisymmetric nozzle flows are presented.