An extension of the Wiener-Volterra theory to a Poisson-distributed impulse train input was used to characterize the temporal response properties of neurons in primary auditory cortex (AI) of the ketamine-anesthetized cat. Both first- and second-order "Poisson-Wiener" (PW) models were tested on their predictions of temporal modulation transfer functions (tMTFs), which were derived from extracellular spike responses to periodic click trains with click repetition rates of 2-64 Hz. Second-order (i.e., nonlinear) PW fits to the measured tMTFs could be described as very good in a majority of cases (e.g., predictability >or=80%) and were almost always superior to first-order (i.e., linear) fits. In all sampled neurons, second-order PW kernels showed strong compressive nonlinearities (i.e., a depression of the impulse response) but never expansive nonlinearities (i.e., a facilitation of the impulse response). In neurons with low-pass tMTFs, the depression decayed exponentially with the interstimulus lag, whereas in neurons with band-pass tMTFs, the depression was typically double-peaked, and the second peak occurred at a lag that correlated with the neuron's best modulation frequency. It appears that modulation-tuning in AI arises in part from an interplay of two nonlinear processes with distinct time courses.