The mammalian inner ear combines spectral analysis of sound with multiband dynamic compression. Cochlear mechanics has mainly been studied using single-tone and tone-pair stimulation. Most natural sounds, however, have wideband spectra. Because the cochlea is strongly nonlinear, wideband responses cannot be predicted by simply adding single-tone responses. We measured responses of the gerbil basilar membrane to single-tone and wideband stimuli and compared them, while focusing on nonlinear aspects of the response. In agreement with previous work, we found that frequency selectivity and its dependence on stimulus intensity were very similar between single-tone and wideband responses. The main difference was a constant shift in effective sound intensity, which was well predicted by a simple gain control scheme. We found expansive nonlinearities in low-frequency responses, which, with increasing frequency, gradually turned into the more familiar compressive nonlinearities. The overall power of distortion products was at least 13 dB below the overall power of the linear response, but in a limited band above the characteristic frequency, the power of distortion products often exceeded the linear response. Our results explain the partial success of a "quasilinear" description of wideband basilar membrane responses, but also indicate its limitations.