1. Development of models of the manner in which interaural intensity differences (IIDs), the major binaural cue for the azimuthal location of high-frequency sounds, are coded by populations of neurons requires knowledge of the extent to which the IID sensitivity of individual neurons is invariant with changes in sound pressure level (SPL) and other stimulus parameters. To examine this issue, recordings were obtained from a large sample (n = 458) of neurons with characteristic frequency (CF) > 3 kHz in the central nucleus of the inferior colliculus (ICC) of anesthetized cats. The sensitivity of IIDs and the effects of changes in SPL on this sensitivity were examined in neurons receiving excitatory contralateral input and inhibitory or mixed inhibitory/facilitatory ipsilateral input (EI neurons). 2. The form of an EI neuron's IID sensitivity and the effects of changes in SPL on that sensitivity were found to be determined in part by the characteristiscs of the neuron's rate-intensity function for monaural contralateral stimulation, and detailed rate-intensity functions were therefore obtained for 91 neurons. Many ICC neurons have nonmonotonic rate-intensity functions, the proportion so classified depending on the criterion of nonmonotonicity employed. 3. IID sensitivity functions for CF tonal stimuli were obtained at one or more intensities for 90 neurons, using a method of generating IIDs that kept the average binaural intensity (ABI) of the stimuli at the two ears constant. In the standard ABI range in which a function was obtained for each unit, the majority of EI neurons (72%) had monotonic (sigmoidal) or near-monotonic IID sensitivity functions. The remainder had nonmonotonic (peaked) IID sensitivity functions, which were attributable either to mixed inhibitory and facilitatory ipsilateral influences or to the fact that the effects of ipsilateral stimulation were superimposed on nonmonotonic effects of changes in intensity at the excitatory ear. 4. IID sensitivity was examined at two or more ABIs (3-5 in most cases) for 40 neurons classified as having monotonic or near-monotonic functions in the standard ABI range and for 7 neurons classifed as nonmonotonic. For a small proportion of neurons with monotonic IID sensitivity functions, the form of the function was relatively invariant with changes in ABI. In those monotonic neurons in which the form of the IID sensitivity function varied with changes in ABI, the most common type of variation was that the position of the sloping portion of the function shifted systematically in the direction of larger IIDs favoring the ipsilateral ear as ABI increased. Neurons with nonmonotonic IID sensitivity functions generally showed marked changes in the form of sensitivity with changes in ABI; as reported by others, some of these neurons are nonmonotonic with respect to both IID and ABI, and this dual nonmonotonicity means that maximum discharge is associated with a particular combination of restricted IID and ABI ranges. Quantitative measures of the variation in IID sensitivity with changes in ABI indicate that, if a conservative criterion of invariance is employed, only 11-23% of IID-sensitive neurons could be regarded as having intensity-invariant sensitivity. Comparison with free-field data on the spatial sensitivity of ICC neurons indicates that a similarly small proportion show intensity-invariant azimuthal sensitivity. 5. For a small sample of neurons, IID sensitivity was also examined for off-CF tonal stimuli and for a broad-band noise stimulus. For most of these neurons, IID sensitivity with these stimuli was similar to that at CF, but in some cases there were marked differences in sensitivity. 6. EI and monaural neurons were intermingled in the ventral region of ICC, with a tendency for EI neurons to occur in clusters. In horizontal penetrations within restricted frequency-band regions, EI cells isolated caudally were characterized by weak inhibition, whereas those isolated rostrally were characterized by strong inhibition. This and related observations suggest that there might be a caudorostral topography of IID sensitivity in ICC of the cat. 7. The fact that most IID-sensitive neurons are also sensitive to ABI means that the population pattern of activity associated with any particular IID would vary with intensity unless the representation of IID were restricted to the small proportion of neurons with intensity-invariant IID sensitivity. Alternatively, as argued by Semple and Kitzes, a place code for IID might be provided by those neurons with dual nonmonotonicity.