1. Spike rates of cells in the cat's lateral superior olive (LSO) depend on interaural level differences (ILDs) and envelope interaural time differences (ITDs) of amplitude-modulated tones presented to both ears. We previously proposed that these sensitivities arise from a common mechanism, which is the IE binaural interaction (Inhibited by the contralateral and Excited by the ipsilateral ear). As a further test of that proposal and to gain a better understanding of the importance of this ITD-sensitivity, responses to monaural and binaural modulation are compared here over a range of modulation frequencies. 2. At low modulation frequencies, LSO-IE cells respond maximally when the envelopes of the amplitude-modulated stimuli at the two ears are out-of-phase by a half-cycle. This phase difference changes in a systematic way, which varies from cell to cell, when modulation frequency is increased. Mean interaural phase, measured over a range of modulation frequencies, was subjected to a characteristic delay analysis. Two measures were extracted: characteristic delay, which reflects differences in conduction delay between ipsi- and contralateral pathways, and characteristic phase, which reflects their sign of interaction. Most characteristic delays were within the physiological range of ITDs. There was a small bias toward positive delays, indicating a longer conduction time for the contralateral pathway. Characteristic phases were tightly distributed approximately 0.5 cycles, consistent with the proposed IE mechanism for ITD-sensitivity. 3. Increases in the modulation frequency of binaural stimuli beyond approximately 300 Hz consistently caused a profound decrease in average spike rate, as well as a decrease in the modulation of spike rate by ITD. The upper limit of ITD-sensitivity was 800 Hz. Sensitivity to envelope ITDs therefore is limited to a much lower range of frequencies than sensitivity to ITDs in fine-structure, e.g., as found in the medial superior olive (MSO), which operates up to several kilo Hertz. 4. A small sample of high-frequency EE cells (excited by both ears) in MSO also was tested with binaural amplitude-modulated stimuli. MSO-EE cells showed weak envelope ITD-sensitivity over a limited range of modulation frequencies. Consistent with the EE interaction, characteristic phases clustered approximately 0 cycles. 5. Mean interaural phase was compared with the phase of responses to monaural modulation. The difference between the ipsilateral and contralateral phases correlated well with the phase measured binaurally, both for LSO and MSO cells. 6. Many features of LSO-IE responses were mimicked by the simplest possible computer model, consisting of subtraction and rectification of low-pass filtered envelope waveforms. Differences between model and physiological results are suggestive of a temporal limitation in the binaural interaction that creates the ITD-sensitivity. 7. These results provide additional evidence for LSO ITD-sensitivity paralleling human psychophysical results. The stimulus boundaries within which ITD-sensitivity occurs suggest that it has a limited role in free-field conditions. It is traditionally thought that, to contribute to the perceived change in spatial location of a sound source, the LSO needs to show a change in overall firing rate summed across cells. This is achieved with small ILDs, but requires large ITDs, because the latter cue is less potent in single cells and has varied effects across cells by virtue of differences in characteristic delay.