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In the attempt of formal pragmatics to capture discourse structure and discourse coherence two main types of theories have emerged: rhetorical relation based theories and question under discussion based theories. In linguistic research question under discussion (QUD) based theories of discourse in the sense of van Kuppevelt (1995a,b) and (Roberts, 1996, 2012) have proven to be highly useful to capture meaning contributions of natural language expressions and constructions in terms of small-scale discourse structure representations. As a larger scale discourse model, however, such theories have been widely considered inferior to theories of discourse structure based on rhetorical relations such as Mann & Thompson (1988a), Asher (1993a), Asher & Lascarides 2003. In this paper I extend QUD-theories to full-scale discourse models comparable with rhetorical relations based theories both in empirical coverage and formal explicitness. While QUD-based theories will still have problems capturing a useful notion of discourse coherence, I argue that question based models have conceptual and empirical advantages as compared to theories of rhetorical structure when it comes to fine-grained analysis of linguistic phenomena, thus they should be used to complement rhetorical structure based theories.