The input/output functions of the different-latency components of human transient-evoked and stimulus-frequency otoacoustic emissions are analyzed, with the goal of relating them to the underlying nonlinear dynamical properties of the basilar membrane response. Several cochlear models predict a cubic nonlinearity that would yield a correspondent compressive response. The otoacoustic response comes from different generation mechanisms, each characterized by a particular relation between local basilar membrane displacement and otoacoustic level. For the same mechanism (e.g., reflection from cochlear roughness), different generation places would imply differently compressive regimes of the local basilar membrane dynamics. Therefore, this kind of study requires disentangling these contributions, using suitable data acquisition and time-frequency analysis techniques. Fortunately, different generation mechanisms/places also imply different phase-gradient delays, knowledge of which can be used to perform this task. In this study, the different-latency otoacoustic components systematically show differently compressive response, consistent with two simple hypotheses: (1) all emissions come from the reflection mechanism and (2) the basilar membrane response is strongly compressive in the resonance region and closer to linear in more basal regions. It is not clear if such a compressive behavior also extends to arbitrarily low stimulus levels.