Non-speaking people who use Augmentative and Alternative Communication (AAC) systems typically have low rates of communication which reduces their ability to interact with others. Research and development continues in the quest to improve the effectiveness of AAC systems in terms of communication rate and impact. One strategy involves making the basic unit of communication an entire utterance, and designing the AAC system to make the storage, retrieval and production of utterances as easy and efficient as possible. Some approaches take this further and include texts, narratives and/or multimedia material for use in conversation. AAC systems operating in such a manner require a structure for containing and managing conversational material and supporting the production of output during conversation. Ideally such a structure should be modelled on the way actual conversations proceed. A number of partial models for this have been presented thus far. These are reviewed in the paper and an integrated model is then proposed that includes both the structure of a conversation and the way in which an AAC system might produce conversational output (e.g. utterances, texts, multimedia items or combinations of these). Modelling the process in this way gives a structure with which an AAC system can organize the support and guidance that it offers to the person using the system. The paper concludes with consideration of three areas of development for further investigation.