Segmented Discourse Representation Theory (SDRT) provides a dynamic semantics for discourse that exploits a rich notion of discourse structure. According to SDRT, a text is segmented into constituents related to each other by means of rhetorical relations; the resulting structure, known as a segmented discourse representation structure or SDRS has various semantic effects. This theory has shown how discourse structure makes contributions to the interpretation of a variety of linguistic phenomena, including tense, modality, presupposition, the interpretation of anaphoric pronouns and ellipsis. SDRT exploits dynamic semantics to interpret SDRSs. We investigate here the advantages of integrating SDRT within continuation style semantics.