Both language and music consist of sequences that are structured according to syntactic regularities. We used two specific event-related brain potential (ERP) components to investigate music-syntactic processing in children: the ERAN (early right anterior negativity) and the N5. The neural resources underlying these processes have been posited to overlap with those involved in the processing of linguistic syntax. Thus, we expected children with specific language impairment (SLI, which is characterized by deficient processing of linguistic syntax) to demonstrate difficulties with music-syntactic processing. Such difficulties were indeed observed in the neural correlates of music-syntactic processing: neither an ERAN nor an N5 was elicited in children with SLI, whereas both components were evoked in age-matched control children with typical language development. Moreover, the amplitudes of ERAN and N5 were correlated with subtests of a language development test. These data provide evidence for a strong interrelation between the language and the music processing system, thereby setting the ground for possible effects of musical training in SLI therapy.