This paper deals with the representation of dialogue, including the semantic aspects. We have been working on a real speech corpus of route explanation dialogues. The paper follows the tradition of dynamic semantics (Kamp and Reyle 1993), and we will use the SDRT of (Asher 1993) which proposes a treatment of the semantic-pragmatic interface. Dynamic semantic theories have traditionally focused on discourse issues, but a few studies have begun to look at dialogue within that framework in the past few years. (Asher and Lascarides 1998). To the rhetorical and intentional structure proposed by SDRT we add a ”topic structure” closely related to the informational structure.