A brief flash presented physically aligned with a moving stimulus is perceived to lag behind, a well studied phenomenon termed the Flash-Lag Effect (FLE). It has been recently shown that the FLE also occurs in audition, as well as cross-modally between vision and audition. The present study has two goals: to investigate the acoustic and cross-modal FLE using a random motion technique; and to investigate whether neural latencies may account for the FLE in general. The random motion technique revealed a strong cross-modal FLE for visual motion stimuli and auditory probes, but not for the other conditions. Visual and auditory latencies for stimulus appearance and for motion were measured with three techniques: integration, temporal alignment and reaction times. All three techniques showed that a brief static acoustic stimulus is perceived more rapidly than a brief static visual stimulus, while a sound source in motion is perceived more slowly than a comparable visual stimulus. While the results of these three techniques agreed closely with each other, they were exactly opposite that required to account for the FLE by neural latencies. We conclude that neural latencies do not, in general, explain the flash-lag effect. Rather, our data suggest that neural integration times are more important.