Nonnative processing has been argued to reflect either reduced processing capacity or delayed timing of structural analysis compared to the extraction of lexical/semantic information. The current study simultaneously investigates timing and resource allocation through a time-frequency analysis of the intrinsic neural activity during syntactic processing in native and English-speaking nonnative speakers of French. It involved structurally constrained anaphora resolution in bi-clausal wh-filler-gap dependencies such as Quelle décision à propos de lui est-ce que Paul a dit que Lydie avait rejetée sans hésitation? ‘Which decision about him did Paul say that Lydie rejected without hesitation?’. We tested the hypothesis that nonnative speakers may allocate greater resources than native speakers to the computation of syntactic representations based on the grammatical specifications encoded in lexical entries, though both native and nonnative processing involves the immediate application of structural constraints. This distinct resource allocation is likely to arise in response to higher activation thresholds for nonnative knowledge acquired after the first language grammar has been fully acquired. To examine this bias in nonnative neurocognitive processing, we manipulated the wh-filler to contain either a lexically specified noun complement such as à propos de lui ‘about him’ or a non-lexcially specified noun phrase modifier such as le concernant ‘concerning him’. We focused on processing at the intermediate gap site, that is, the point of information exchange between the matrix and the embedded clauses by adopting a measurement window corresponding to the bridge verb dit ‘said’ and subordinator que ‘that’ introducing the embedded clause. Our results showed that structural constraints on anaphora produced event-related spectral perturbations at 13-14Hz early into the presentation of the bridge verb across groups. An interaction of structural constraints on anaphora with group was found at 18-19Hz early into the presentation of the bridge verb. In this interaction, the nonnative-speaker activity at 18-19Hz echoed the concurrent general patterns at 13-14Hz, whereas the native-speaker activity revealed distinct power at 18-19Hz and at 13-14Hz. There was no evidence of delay of structural constraints on intermediate gaps with respect to lexical access to the bridge verb and subordinator. However, nonnative speakers’ allocation of power in cell assembly synchronizations of fillers and gaps at the intermediate gap site reflected the grammatical specifications lexically encoded in the fillers.