1. Rate-level functions for individual cochlear nerve fibers of the alligator lizard, Gerrhonotus multicarinatus, were generated by measuring a fiber's driven discharge rate (the difference between the average discharge rates in the presence and absence of a tone burst) as a function of sound pressure level. 2. When plotted in double logarithmic coordinates, the rate-level function approaches a straight line at low sound pressure levels and saturates at high levels. Thus the rate-level function is a saturating power function of sound pressure. We developed an algorithm to estimate the exponent of the straight-line portion of the function. When tested on simulated data with known parameters, the algorithm provided unbiased estimates of the exponent. 3. Nerve fibers innervating two distinct regions of the alligator lizard's auditory organ, the free-standing region and the tectorial region, have differing rate-level functions. 4. The mean exponent estimate of the rate-level functions of fibers innervating the free-standing region is approximately 2 at all frequencies. For stimulus frequencies at the characteristic frequency (CF), the mean value was 2.1 +/- 0.10 (SE, n = 131). For stimulus frequencies above and below CF, the mean exponent estimates were 2.1 +/- 0.13 (n = 49) and 2.1 +/- 0.11 (n = 34), respectively. A value of 2 is expected for a broad class of nonlinear systems. 5. The mean exponent estimates of the rate-level functions of fibers innervating the tectorial region were 3.0 +/- 0.30 (n = 32) for stimulus frequencies at CF, 2.5 +/- 0.33 (n = 3) for stimulus frequencies below CF, and 1.0 +/- 0.21 (n = 16) for stimulus frequencies above CF. Both the deviation from square-law behavior at CF and the frequency dependence of the exponent imply that nonlinear processing in the tectorial region differs intrinsically from that in the free-standing region. 6. For free-standing fibers, the saturation rate of the rate-level function (the maximum driven rate) is independent of stimulus frequency. This suggests that, in the free-standing region, 1) the alternating (AC) component of the receptor potential makes no significant contribution to the average rate of discharge and 2) neural saturation results from a process that occurs after the narrow-band frequency-selective process(es). 7. In tectorial fibers, the saturation rate is a bandpass function of sound frequency, with a broad peak between 150 and 300 Hz. This function appears to be common to all tectorial fibers.(ABSTRACT TRUNCATED AT 400 WORDS)