The auditory temporal integration function was studied with the objective of improving both its quantitative description and the specification of its principle independent variable, stimulus duration. In Sec. I, temporal integration data from 20 studies were subjected to uniform analyses using standardized definitions of duration and two models of temporal integration. Analyses revealed that these data were best described by a power function model used in conjunction with a definition of duration, termed assigned duration, that de-emphasized the rise/fall portions of the stimuli. There was a strong effect of stimulus frequency and, in general, the slope of the temporal integration function was less than 10 dB per decade of duration; i.e., a power function exponent less than 1.0. In Sec. II, an experimental study was performed to further evaluate the models and definitions. Detection thresholds were measured in 11 normal-hearing human subjects using a total of 24 single-burst and multiple-burst acoustic stimuli of 3.125 kHz. The issues addressed are: the quantitative description of the temporal integration function; the definition of stimulus duration; the similarity of the integration processes for single-burst and multiple-burst stimuli; and the contribution of rise/fall time to the integration process. A power function in conjunction with the assigned duration definition was again most effective in describing the data. Single- and multiple-burst stimuli both seemed to be integrated by the same central mechanism, with data for each type of stimulus being described by a power function exponent of approximately 0.6 at 3.125 kHz. It was concluded that the contribution of the rise/fall portions of the stimuli can be factored out from the rest of the temporal integration process. In Sec. III, the conclusions that emerged from the review of published work and the present experimental work suggested that auditory temporal integration is best described by a power function in conjunction with the assigned duration definition. The exponent for the power function is typically less than 1.0, and varies with frequency and hearing level. Second, a means of empirically assaying the contribution of the rise-fall portions of the stimuli is presented and evaluated. Finally, properties of a central auditory integrator are hypothesized.(ABSTRACT TRUNCATED AT 250 WORDS)