Early reports of audiovisual (AV) multisensory integration (MI) indicated that unisensory stimuli must evoke simultaneous physiological responses to produce decreases in reaction time (RT) such that for unisensory stimuli with unequal RTs the stimulus eliciting the faster RT had to be delayed relative to the stimulus eliciting the slower RT. The "temporal rule" states that MI depends on the temporal proximity of unisensory stimuli, the neural responses to which must fall within a window of integration. Ecological validity demands that MI should occur only for simultaneous events (which may give rise to non-simultaneous neural activations). However, spurious neural response simultaneities which are unrelated to singular environmental multisensory occurrences must somehow be rejected. Using an RT/race model paradigm we measured AV MI as a function of stimulus onset asynchrony (SOA: ±200 ms, 50 ms intervals) under fully dark adapted conditions for visual (V) stimuli that were either weak (scotopic 525 nm flashes; 511 ms mean RT) or strong (photopic 630 nm flashes; 356 ms mean RT). Auditory (A) stimulus (1000 Hz pure tone) intensity was constant. Despite the 155 ms slower mean RT to the scotopic versus photopic stimulus, facilitative AV MI in both conditions nevertheless occurred exclusively at an SOA of 0 ms. Thus, facilitative MI demands both physical and physiological simultaneity. We consider the mechanisms by which the nervous system may take account of variations in response latency arising from changes in stimulus intensity in order to selectively integrate only those physiological simultaneities that arise from physical simultaneities.