Nonlinearities affecting cochlear mechanics produce appreciable compression in the basilar membrane (BM) input/output (I/O) functions at the characteristic frequency for sound-pressure levels (SPLs) as low as 20 dB (re: 20 mu Pa). This is thought to depend upon saturation of the outer hair cell (OHC) mechanoelectrical transducer (MET). This hypothesis was tested by solving a nonlinear integrodifferential equation that describes the BM vibration in an active cochlea. The equation extends a previously developed linear approach [Mammano and Nobili, J. Acoust. Sec. Am. 93, 3320-3332 (1993)], here modified to include saturating MET, with a few corrections mainly concerning tectorial membrane resonance and OHC coupling to the BM. Stationary solutions were computed by iteration in the frequency domain for a wide range of input SPLs, generating BM I/O functions, frequency response envelopes, and two-tone distortion products. Traveling-wave amplitude envelopes were also computed for a fixed suppressor and several suppressed tones in order to evidence the phenomenon of two-tone suppression (frequency masking) at the mechanical level. All results accord nicely with experimental data.