Previous papers have shown that the shapes of rate-intensity functions of auditory nerve fibres vary with spontaneous rate (Sachs and Abbas 1974; Sachs et al. 1989; Winter et al. 1990; Yates et al. 1990), and that the variation is due to the nonlinear properties of the basilar membrane. This paper examines the basilar membrane nonlinearity and provides a semi-quantitative explanation for it in terms of previous models (Zwicker 1979; Patuzzi et al. 1989) and an analogue model. It thereby provides explanations for the shapes of the basilar membrane input-output curves and for the way in which they vary with trauma. The shapes of the neural rate-intensity functions are quantified and shown to be consistent with the low-threshold data of Geisler et al. (1985). Several nonlinear properties of the cochlea, such as recruitment, are also interpreted.