Data from first‐order auditory fibers are modeled as a simple renewal process. The interarrival times of neural spikes are treated as a geometric process at multiples of the period of the input signal modified by some temporal jitter, characterized as a frequency‐dependent random variable with a standard deviation proportional to a small fraction of the period of the waveform. Two classes of models are considered: a timing model in which psychophysical decisions are based on the time taken to obtain a predetermined number of counts on many parallel channels, and a counting model in which psychophysical decisions are based on the number of neural events that occur within some fixed time on many parallel channels. For both models it is assumed that the geometric parameter is monotonically a power function of signal intensity, that the threshold criterion of activity in a channel is independent of frequency, and that the number of channels is independent of both signal intensity and frequency. Predictions concerning the discrimination of change in frequency and intensity of a sinusoid are derived. Existing data, both for intensity and frequency, are sufficiently consistent to reject the timing model (which one would expect from other considerations), but they are not sufficiently consistent to provide either a strong test of the counting model or sharp estimates of the parameters of the model.