The application of a particular branch of non-linear system analysis, the functional series expansion or integral method, to the auditory system is reviewed. Both the Volterra and Wiener approach are discussed and an extension of the Wiener method from its traditional white-noise stimulus approach to that of Poisson distributed clicks is presented. This type of analysis has been applied to compound and single-unit responses from the auditory nerve, cochlear nucleus, auditory midbrain and medial geniculate body. Most studies have estimated only first-order Wiener kernels but in recent years second-order Wiener and Volterra kernels have been estimated, particularly with reference to dynamic non-linearities. A particular form of second-order analysis, the Spectro Temporal Receptive Field, offers an alternative to first-order cross-correlation when phase-lock is absent. The correlation method has revealed that neural synchronization is less affected by intensity changes and damage to the hair cells than is neural firing rate. Although the presence of the static cochlear non-linearity could be demonstrated on the basis of the intensity dependence of the first-order Wiener kernel, the identification of the exact form of the nonlinearity of the peripheral auditory system on basis of higher-order Wiener kernels has so far been inconclusive. However, successes of the method can be found in the description of the dynamic non-linearities and non-linear neural interactions.