Although many properties of click responses can be accounted for by a single, frequency-dispersive traveling wave exciting a single, characteristic-frequency (CF) resonance, some properties, such as waxing and waning cannot. Joint time–frequency distributions (TFDs) were used to help understand click responses of cat single auditory-nerve (AN) fibers (CFs<4 kHz) and published measurements of chinchilla basilar-membrane (BM) motion. For CFs>800 Hz, the peak energy of the response decreased in latency and frequency as the level increased, as expected. However, at high levels the trend reversed for AN, but not BM, responses. Normalized TFDs, which show the frequency with the peak energy at each response time, revealed glides, as previously reported. Classical theory predicts smooth, upward glides. Instead, at low CFs there were downward glides, and at other CFs glides had substantial irregularities. Finally, click skirts, defined as the longest-latency part of click responses, sometimes showed deviations from CF for above-threshold sound levels. Most of these phenomena are not explained by a single, frequency-dispersive traveling wave exciting a single CF resonance, but they can be accounted for by the interaction of two (or more) excitation drives with different latencies and frequency contents. © 2004 Acoustical Society of America.