The fundamental determinacy of linguistically encoded meaning has remained as a tacit assumption underlying much work in the study of interlingual interpreting and interpreter behaviour. When confronted with the real-time, on-line nature of interpreter-mediated crosscultural encounters, however, such a view rapidly becomes untenable and an alternative model of the retrieval and representation of meanings becomes necessary. Adopting a relevance theoretic account of interpreter-mediated communication but also drawing on some insights from conversation analysis, this article examines evidence of participant moves – and particularly interpreter moves – to show inferencing at work and the evolving, intra-interactional nature of context. Indeed, a central contention is that interpreters’ performance can provide explicit evidence of take-up, of the sense they make of others’ talk and how they respond to it, in a process of joint negotiation of contextual assumptions. However, whereas mutual accessibility of such assumptions would seem to be a precondition for establishing relevance, the evidence presented here suggests that divergent contexts may emerge among participants, even though the ‘speech-exchange system’ (Schegloff, 1999) of interpreter mediation appears to proceed in an unproblematic way.