A computational model was developed to simulate the responses of auditory-nerve (AN) fibers in cat. The model's signal path consisted of a time-varying bandpass filter; the bandwidth and gain of the signal path were controlled by a nonlinear feed-forward control path. This model produced realistic response features to several stimuli, including pure tones, two-tone combinations, wideband noise, and clicks. Instantaneous frequency glides in the reverse-correlation (revcor) function of the model's response to broadband noise were achieved by carefully restricting the locations of the poles and zeros of the bandpass filter. The pole locations were continuously varied as a function of time by the control signal to change the gain and bandwidth of the signal path, but the instantaneous frequency profile in the revcor function was independent of sound pressure level, consistent with physiological data. In addition, this model has other important properties, such as nonlinear compression, two-tone suppression, and reasonable Q10 values for tuning curves. The incorporation of both the level-independent frequency glide and the level-dependent compressive nonlinearity into a phenomenological model for the AN was the primary focus of this work. The ability of this model to process arbitrary sound inputs makes it a useful tool for studying peripheral auditory processing.