In this paper we discuss the use of discourse context in spoken dialogue systems and argue that the knowledge of the domain, modelled with the help of dialogue topics is important in maintaining robustness of the system and improving recognition accuracy of spoken utterances. We propose a topic model which consists of a domain model, structured into a topic tree, and the Predict-Support algorithm which assigns topics to utterances on the basis of the topic transitions described in the topic tree and the words recognized in the input utterance. .