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Automatic analysis of spoken conversations has recently searched for phenomena like agreement/disagreement in collaborative and non-conflictual discussions (e.g., meetings). This work adds a novel dimension investigating conflicts in spontaneous conversations. The study makes use of broadcasted political debates where conflicts naturally arise between participants. In the first part, an annotation scheme to rate the degree of conflict in conversations is described and applied to 12 hours of recordings. In the second part, the correlation between various prosodic/conversational features and the degree of conflict is investigated. In the third part, we perform automatic detection of the level of conflict based on those features showing an F-measure of 71.6% in three-level classification tasks.