The interleaving peak structure of poststimulus time (PST) histograms of low‐frequency cochlear‐nerve‐fiber responses to acoustic clicks of both polarities implies that a cochlear neuron is excited by a damped oscillatory waveform, referred to here as a click excitation function (CEF) that is half wave rectified. For a stimulus consisting of two closely spaced clicks, the amplitude and delay of the second click relative to the first click can be adjusted so that one‐half cycle of the CEF due to the first click nulls or cancels a particular half‐cycle of the other CEF. A null produced in this manner can be detected from the PST histograms of responses of a particular fiber to both polarities of the click‐pair stimulus. This nulling technique has been used to study the responses of cochlear nerve fibers to combination click stimuli. Details of these measurements are given, and the interpretation of the results leads to the consideration of two apparently different nonlinear phenomena. These results and the techniques used to obtain them provide a means by which certain constraints on the mechanisms of the peripheral auditory system can be evaluated.