A complete understanding of the accuracy for describing function methods for nonlinear stochastic systems is obtained in terms of a 'filtering hypothesis’. The insight gained is exploited to justify the use of ∥ΦgΦω∥2as a measure of error in approximating non-linear systems. The non-linear quadratic gaussian (NLQG) design methodology is shown to be consistent with the use of describing functions being reasonably accurate. Various approximation schemes for estimating the accuracy of linearized representations of non-linear systems are developed. It is concluded that a systematic approach to the use of describing functions has been developed and that they constitute a useful approach to a wide range of non-linear systems.