Conflict monitoring, which is a process that detects conflict and initiates control processes to resolve said conflict, is assumed to be implemented in production-based language control. As conflict monitoring is a domain-general process, it should follow that it is also implemented in bilingual language comprehension. However, conflict monitoring is not explicitly implemented in models of bilingual language comprehension. With a bilingual flanker task, we investigated the Congruency Sequence Effect (CSE), which is a marker of conflict monitoring, in a bilingual language comprehension context. The results showed a congruency effect, but no CSE with the bilingual flanker, whereas both a congruency effect and CSE were observed with a non-linguistic numerical flanker. This pattern indicates that conflict monitoring might not arise in bilingual language comprehension.