The integration of nonsimultaneous frequency components into a single virtual pitch was investigated by using a pitch matching task in which a mistuned 4th harmonic (mistuned component) produced pitch shifts in a harmonic series (12 equal-amplitude harmonics of a 155-Hz F0). In experiment 1, the mistuned component could either be simultaneous, stop as the target started (pre-target component), or start as the target stopped (post-target component). Pitch shifts produced by the pre-target components were significantly smaller than those obtained with simultaneous components; in the post-target condition, the size of pitch shifts did not decrease relative to the simultaneous condition. In experiment 2, a silent gap of 20, 40, 80, or 160 ms was introduced between the nonsimultaneous components and the target sound. In the pre-target condition, pitch shifts were reduced to zero for silent gaps of 80 ms or longer; by contrast, a gap of 160 ms was required to eliminate pitch shifts in the post-target condition. The third experiment tested the hypothesis that, when post-target components were presented, the processing of the pitch of the target tone started at the onset of the target, and ended at the gap duration at which pitch shifts decreased to zero. This hypothesis was confirmed by the finding that pitch shifts could not be observed when the target tone had a duration of 410 ms. Taken together, the results of these experiments show that nonsimultaneous components that occur after the onset of the target sound make a larger contribution to the virtual pitch of the target, and over a longer period, than components that precede the onset of the target sound.