Recent neurophysiological experiments make it clear that some neurons in the auditory systems of the cat and monkey are responsive to interaural time differences that are larger than the maximum value possible for animals with their headwidths. Discussed here are several possible ways such neurons could be activated in real‐world situations, and it is suggested that these neurons might be involved in the suppression of erroneous localization information, the suppression of reverberation, and/or in the analysis for periodicities in the acoustic stimulus.