Auditory event-related brain potentials evoked in response to tone stimuli and to speech stimuli were recorded in a group of parents of children with specific language-impairment and a group of parents of normally speaking children. The parents of the language-impaired children showed longer P3 latencies than the parental control group in the speech task requiring a phonological discrimination, but did not differ from the controls in the linguistically non-demanding tone discrimination task. The longer P3 latency was associated with a positive parental history of language delay. There were no group differences concerning the N1 component in any of the tasks. The findings indicate that parents of children with specific language impairment show signs of deficient late-stage perceptual higher order linguistic processing, whereas the earlier central sensory detection stage of the phonological information is no different from the controls. Our observations are particularly interesting with regard to a study of the children of these two parental groups, where the language-impaired children showed longer P3 latencies than controls in both a tone task and a speech task, whereas there were no differences between the children concerning the N1 component. We propose that deficient late-stage auditory higher order perceptual processing as indexed by the longer P3 latency to speech stimuli observed both in children with specific language-impairment and in their parents may represent a constitutional trait, contributing to the language acquisition difficulties in these children.