This study examines interactional sequences in which students make assertions about topic-relevant matters in classroom interactions. Using a Conversation Analytical approach, I show how the students’ knowledge claims lead to negotiations of sequential and epistemic rights to make such claims. Through these negotiations, the students upgrade their epistemic stance by repeating or backing their claims with accounts and providing evidence of them. The teachers’ acceptance or rejection of the students’ initiatives displays an orientation to the sequential and topical relevance of the information provided by the students. This study contributes to a better understanding of student initiatives in the classroom, a topic that until now has received scarce attention. Additionally, it contributes knowledge about the negotiation of epistemic authority in relation to assertions and their responses, which may have more general implications for the study of talk-in-interaction.