A sufficient condition for local stability of the spatially discretized model of a class of non-linear distributed parameter systems is derived using the circle criterion for stability and bounded-input, bounded-output stability. As a physical system the catalytic packed-bed tubular reactor is taken to illustrate the application of the theorem to process control systems. The stability condition in the large derived from non-linear system equations is compared with the stability condition in the small derived from linearized system equations. Interpretations of the result are given in terms of physical variables.