When an infrequent or unexpected stimulus is presented to the adult, a characteristic enhancement of the late positive component (LPC) of the averaged evoked cortical potential is observed. To test whether this effect obtains near birth, we presented low and high probability visual stimuli to 29 3-month-old infants in two studies. In Study 1, electrical potentials were recorded from occipital and parietal scalp sites (Oz and Opz), and in Study 2 also from a frontal lead (Fz). A clear LPC effect was observed over the posterior regions between 300-600 msec following the onset of the infrequent stimulus. This is the first demonstration of an LPC effect in infants, reflecting cognitive processing involving memory. A linear discriminant analysis was used to analyze the nature of the LPC effect on single trials. A local probability index (LPI) was calculated to examine the effects of prior presentations of familiar events on the infants' responses to specific occurrences of unfamiliar events. The LPC occurred more frequently for those unfamiliar trials preceded by a sequence of three or more familiar stimuli than by only one or two. Thus, single trial analysis of infant evoked potentials provides an opportunity to assess trial-to-trial variation in the brain's responses to rapidly changing events.