Interruption has predominantly been conceptualised as a violation of normative turn-taking practices and speakership rights. The present study further develops a broader perspective by showing that speakers can orient to matters of sequential organisation, other than turn-taking, when they claim their own talk is interruptive. Drawing from a larger collection of 72 cases where explicit claims to interruption were made, this paper uses conversation analysis to examine a subset of 20 instances where speakers specifically described what they were doing was interruption. Our target phenomenon was expressions such as “I want to interrupt” and “apologise for interrupting”. Speakers can prospectively mark some upcoming talk as interruptive and they can also retrospectively cast what they have just said as an interruption. Either way, the observably relevant disruption was not to turn-taking but to other sequences of action, namely the proper order of activities, the organisation of topics and adjacency pairs. Furthermore, by focusing on cases from institutional settings we propose that by explicitly claiming one's own talk as interruptive participants make relevant membership categories and their associated deontic responsibilities for the progression of activities within institutional settings.