A method is presented for estimating parameters of chemical reactor models. It is assumed that the process can be represented by a system of quasilinear partial differential equations, with two-point boundary values. The Green's function is used to transform the differential to integral equations. The unknown coefficients can then be identified by gradient search. The algorithm of the Fast Fourier Transform may be used to numerically compute some of the integrals involved. The FFT, sharply reducing the computation time, makes the method effective. Numerical applications are dealt with in detail, showing that the method is promising.