Purpose: One possible source of tense and agreement limitations in children with specific language impairment (SLI) is a weakness in appreciating structural dependencies that occur in many sentences in the input. This possibility was tested in the present study. Method: Children with a history of SLI (H-SLI; n = 12; M = 9;7 [years;months]) and typically developing same-age peers (TD; n = 12; M = 9;7) listened to and made grammaticality judgments about grammatical and ungrammatical sentences involving either a local agreement error (e.g., "Every night they talks on the phone") or a long-distance finiteness error (e.g., "He makes the quiet boy talks a little louder"). Electrophysiological (ERP) and behavioral (accuracy) measures were obtained. Results: Local agreement errors elicited the expected anterior negativity and P600 components in both groups of children. However, relative to the TD group, the P600 effect for the long-distance finiteness errors was delayed, reduced in amplitude, and shorter in duration for the H-SLI group. The children's grammaticality judgments were consistent with the ERP findings. Conclusion: Children with H-SLI seem to be relatively insensitive to the finiteness constraints that matrix verbs place on subject-verb clauses that appear later in the sentence.