We asked to what extent the respective gaze direction influences (i) the spatial congruence of perceived direction of auditory and visual cues, and (ii) the discrimination of the direction of target motion. With fixed head position, subjects directed their gaze in various positions and localised auditory targets (band-pass noise, 2 kHz) presented at one of nine positions (straight ahead, or four symmetric positions to the left or right separated by 2.75 deg, respectively). Forced-choice judgements, whether the sound was perceived to the left or right of a visual reference light, show that the azimuth of the sound was perceived as slightly shifted to the left of a visual reference when the gaze was directed to the left, and vice versa. The maximum of this relative auditory - visual shift was 4.7 deg over a range of 45 deg (left or right) of gaze directions. In (ii), a spot of light started at the centre of a monitor and moved at 2 or 12 deg s−1 leftward or rightward. Subjects reported the direction by pressing a key; their gaze was directed at 0, 8, or 16 deg to the left or right. Mean choice-reaction times increased with increasing gaze eccentricity, but differently depending on stimulus direction and speed: with left fixation they were shorter for leftward than rightward motion; with right fixation they were shorter for rightward motion. This effect was stronger for the slow than for the fast stimulus speed. Thus, facilitation occurs when stimuli move with moderate velocity toward the direction of gaze. While the auditory-visual shift in (i) may reflect an incomplete transformation of spatial (craniocentric and oculocentric) coordinates as suggested by recordings in the primate midbrain, the results in (ii) conform with reports of specialised units in the posterior parietal cortex (areas LIP, 7a, MST) that, in registering oculomotor position, modulate visual sensitivity.