A collocation method is given for streamwise integration of stiff, nonlinear reactor models. Perturbation solutions of the model are used as basis functions. Low-order approximations give results analogous to the Method of Steady States, whereas higher approximations give more detailed solutions. The method uses a small set of mesh points, and selects them to minimize global truncation errors; this feature saves computation when the reactor model is complicated. The efficiency of the method is demonstrated by numerical examples for isothermal and adiabatic reactors.