The physical and the psychophysical relationships between interaural time and intensity differences were studied for 24 frequency bands of critical bandwidth covering the full audio range. For the physical investigations a catalogue of outer ear impulse responses for 122 directions of the upper hemisphere was analyzed according to the combinations of interaural time and level differences found in each critical band. From these data curves of "natural combinations" of the interaural parameter differences were determined by the minimum square error method. In a psychoacoustical study it is shown that signals containing "natural" parameter combinations produce response patterns that differ from those produced when signals with contradictory interaural properties have been used. Finally an extension to the powerful binaural model of Lindemann [J. Acoust. Soc. Am. 80, 1608-1622 (1986)] is introduced, taking into account the results of the previous investigations.