Abstract Previous studies on relative clauses have mostly dealt with the restrictive/non-restrictive dichotomy, focusing on the differences from a syntactic point of view. In particular, non-restrictive relative clauses have traditionally been defined negatively, i.e. with reference only to functions they do not have. In this article, evidence is provided for a positive definition of this type of relative clause, which will be labelled here ‘appositive relative clause’ (ARC). A taxonomy is suggested, obtained through the study of a 450-utterance, contextualised corpus. The taxonomy is based on syntactic, semantic, and above all, pragmatic criteria, following Prince's (1981, 1992) definitions of given/new information and Sperber and Wilson's relevance theory (1986). Findings of a survey also show that ARCs are not systematically suppressible and that the differences in suppressibility can be accounted for by the different functions fulfilled by the ARC in discourse.