This article presents two sets of experiments concerning the ability to discriminate changes in the phase spectra of wideband periodic sounds. In the first set, a series of local phase changes is used to modify the envelopes of the waves appearing at the outputs of a range of auditory filters. The size of the local phase change required for discrimination is shown to be strongly dependent on the repetition rate, intensity, and spectral location of the signal. In the second set of experiments, a global phase change is used to produce a progressive phase shift between the outputs of successive auditory filters, without changing the envelopes of the filtered waves. Contrary to what is often assumed, listeners can discriminate between-channel phase shifts once the total time delay across the channels containing the signal reaches 4-5 ms. In this case, however, the discrimination is largely independent of signal parameters other than bandwidth. A highly simplified model of the cochlea, consisting of an auditory filter bank and units that record the times of the larger peaks in the filter outputs, is developed to explain the two contrasting sets of results.