Most neurons in the deep and intermediate layers of the superior colliculus (SC) that respond to acoustic stimuli are sensitive to interaural intensity disparities (IIDs). We examine a model for the generation of sensitivity to IIDs that depends upon temporal coincidence of the inputs from each ear at a given binaural neuron. Because the neural response latency decreases with increasing stimulus intensity, IIDs affect the relative timing of arrival of the inputs. If this model were true, the neurons sensitive to IIDs should also respond to interaural time differences (ITDs) of isointensive stimuli, provided that the magnitude of the delays reflect the neural latency-intensity relationship. For both major classes of binaural cells in the SC, namely those that exhibit binaural inhibition (BI) and binaural facilitation (BF), our results support the model in that the detection of IIDs is largely due to their sensitivity to the temporal overlap of inputs from each ear. The shapes of the IID and ITD functions for each class are similar. The summation of inputs includes inhibitory as well as facilitatory interactions. Estimates of the durations of the subliminal excitatory events in BF cells using the model indicate that they are relatively short (1-4 ms), whereas the durations of the inhibitory processes in BI cells are much longer. The model specifies a common neuronal mechanism for comparison of interaural disparities of time and intensity and does not separate the processing of IIDs and ITDs, as the classic duplex theory suggests. The model provides a physiological explanation for certain features of the psychophysical phenomenon of time-intensity trading. It is also consistent with recent experiments that have shown that the auditory system is sensitive to behaviorally significant ITDs of high-frequency complex signals. The model applies only to the processing of transient stimuli and does not address neural sensitivity to IIDs of continuous high-frequency tones.