AbstractThe current prevalence of conspiracy theories on the internet is a significant issue, tackled by many computational approaches. However, these approaches fail to recognize the relevance of distinguishing between texts which contain a conspiracy theory and texts which are simply critical and oppose mainstream narratives. Furthermore, little attention is usually paid to the role of inter‐group conflict in oppositional narratives. We contribute by proposing a novel topic‐agnostic annotation scheme that differentiates between conspiracies and critical texts, and that defines span‐level categories of inter‐group conflict. We also contribute with the multilingual XAI‐DisInfodemics corpus (English and Spanish), which contains a high‐quality annotation of Telegram messages related to COVID‐19 (5000 messages per language). We also demonstrate the feasibility of an NLP‐based automatization by performing a range of experiments that yield strong baseline solutions. Finally, we perform an analysis which demonstrates that the promotion of intergroup conflict and the presence of violence and anger are key aspects to distinguish between the two types of oppositional narratives, that is, conspiracy versus critical.