Objective To investigate the maturation of long-latency auditory evoked potentials (LLAEP) from 6 to 48months in infants with a family history of language impairment (FH+) and control infants (FH−). Methods LLAEPs of seventeen FH+ infants were compared to 28 FH− infants at 6, 9, 12, 16, 24, 36 and 48months. Participants received a passive oddball paradigm using fast- and slow-rate non-linguistic auditory stimuli and at 36 and 48months completed a battery of standardized language and cognitive tests. Results Overall, the morphology of LLAEP responses differed for fast- versus slow-rate stimuli. Significant age-related changes in latency and amplitude were observed. Group differences, favoring FH− infants, in the rate of maturation of LLAEPs were found. Responses to fast-rate stimuli predicted language abilities at 36 and 48months of age. Conclusions The development of LLAEP in FH+ children is modulated by differences in the rate of maturation as well as variations in temporal processing abilities. Significance These findings provide evidence for the role of non-linguistic auditory processes in early language development and illustrate the utility of using a perceptual-processing skills model to further our understanding of the precursors of language development and impairment.