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This article explores storytelling practices in French ordinary conversations. While storytelling has been a prolific object of investigation across human and social sciences, our focus here is on the contribution of Conversation Analysis. This line of work has shown how storytellings are interactionnally produced through the speakers and recipients turn-by-turn adjustments. After an overview of the main findings of CA research on storytelling, we present a study of story-openings. The study examines the use of informings as a resource for projecting a storytelling to various extents. The study shows that the tellworthiness of a story-to-be is interactionally established through the design features of the informing and the recipient’s verbal and non-verbal displays of alignment and affiliation.