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For pt.IV see ibid., vol.SMC-13, no.5, p.964-72 (1983). The psychophysical properties of a multiple-channel neural-counting model are investigated. Each channel represents a peripheral afferent fiber (or a group of such fibers) and consists of a cascade of signal-processing transformations, each of which has a physiological correlate in the auditory system. The acoustic signal is passed by a mathematical construct (which may be a pure tone or Gaussian noise) through a series of transformations. Spontaneous neural activity is independently incorporated into each channel by means of an additive refractoriness-modified Poisson process. A union process at a more distal center in the nervous system is generated by a parallel collection of such channels with a density (in frequency) determined by the cochlear mapping function. The statistics of the union count (in a fixed time) are then processed at a decision center in a manner that depends on the psychophysical paradigm under consideration. This random count number is assumed to contain all of the information for the examples considered. The model has been used to calculate psychophysical functions for pure-tone loudness estimation, pure-tone and variable-bandwidth noise intensity discrimination, and variable-bandwidth noise loudness summation. The theoretical results are in good agreement with human psychophysical data.