Multi-party human-computer dialogue research is still in its infancy. Most of the research in this respect either addresses dialogues between pairs of computers, or performs studies on multi-party human dialogue corpora, in order to better understand this type of interaction. Thus, there are only a few computational models for this type of linguistic interaction and this paper tries to fill this gap. However, only the issue of generating linguistically-appropriate speech turns in multi-party dialogue will be addressed here. For this, a formal framework that accounts for multi-party dialogue situations is developed. Then this model is customized, so that only the point of view of the machine is considered. Finally, several particularly interesting multi-party dialogue situations (for service-oriented systems) are enforced with algorithms for rhetorical structure updating for answer generation, in natural language, and evaluated on concrete multi-party dialogue examples.