This paper states that well-checked event-related brain potential (ERP) research backs the convergence hypothesis, pursuant to which L2 learners at first vary from native speakers and then approach native-like neurocognitive processing mechanisms. The fact that ERPs in highly proficient late L2 learners are often indiscernible from those of native speakers indicates that age-of-acquisition results in SLA are not chiefly moved by maturational restrictions.