by deriving necessary and sufficient conditions for the stability of nonlinear computing schemes. In ? 1, we motivate the concept of stability to be used here and provide the basic definitions. In ? 2, we prove the main theorem on stability which relates stability to conditions on the Frechet derivatives of the operators. As corollaries of this theorem we obtain Mikhlin's basic results and examine the computing scheme of Vainikko [11]. In ? 3, special cases and examples of the main theorem are given.