This study examined the time course of attentional tuning of the N1 and P3 components of the auditory evoked potential. Human subjects were presented with two concurrent sequences of pure tone stimuli, one sequence delivered to each ear. They were instructed to listen to the tones in one ear and count randomly-embedded target stimuli, identified by pitch, while ignoring concurrent and physically equivalent stimuli in the other ear. Attention was then allocated to other ear-pitch combinations in subsequent runs. The rate of stimulation was rapid, an average of three stimuli per second per channel, to maximize N1 differences between channels. Evoked potentials were sampled at various times during each experimental run, to determine the time course of amplitude change in each auditory channel, as the subject tuned his neural response to the selected stimuli. The results indicated that N1 took 30-45 s to emerge as significantly larger in the attended channel, whereas P3 was instantly larger in the attended channel upon presenting the first rare stimulus of a run. The N1 effect disappeared for standard stimuli after about 7 min of stimulation, despite a continuously high rate of target identification. However, for the rare target stimuli, N1 and P3 remained at a higher level in the attended channel throughout the typical 15 min run. The study concludes that neural selectivity proceeds in a "top-down" manner, with the longer-latency P3 component showing a selective response sooner than N1. In addition, there is evidence that the selectivity of N1 tuning increases over time, with the continued focussing of attention.