Abstract Continuity and discontinuity (maintaining or shifting deictic centres across segments) are important aspects of discourse relations. Yet they have been attributed to these relations in very different ways. This calls for an analysis of individual instances of discourse relations with respect to their continuity dimensions. To this end, we operationalise Givón’s (1993) continuity dimensions ( time, space, reference, action, perspective, modality, and speech act ), decomposing them into distinctive features that allow a consistent and accurate classification of the continuity dimensions in discourse relation tokens. This inventory was applied to five representative relation types ( causal, contrastive, conditional, elaboration, and temporal ) from the RST Discourse Treebank ( Carlson & Marcu 2001 ). We found that relations can simultaneously be more continuous for some dimensions but more discontinuous for others. What is more, discourse relations typically vary widely in different continuity dimensions and thus cannot be described as fully continuous or discontinuous, neither on the level of the entire relation type nor for one of its particular dimensions. Using examples of causal, conditional, and contrastive relations, we also illustrate how the results of our analysis can be used to verify hypotheses about correlations between continuity and discourse relations.