Abstract. Human-computer interfaces require models of dialogue structure that capture the variability and unpredictability within dialogue. In this paper, taking as starting point P systems, and by extending it to the concept of dialogue P systems through linguistic P systems we introduce a multi-agent formal architecture for dialogue modelling. In our model, cellular membranes become contextual agents by the adjunction of cognitive domains. With this method, the passage from the real dialogue to the P systems model can be achieved in a quite intuitive and simple way. MotivationComputational work on discourse has focused both on extended texts and on dialogues. Work on the former is relevant to document analysis and retrieval applications, whereas research on the latter is important for human-computer interfaces. In fact, the development of machines that are able to sustain a conversation with a human being has long been a challenging goal. If we focus on dialogue modelling, we can distinguish two related research goals adopted by researchers on the field: 1) to develop a theory of dialogue and 2) to develop algorithms and procedures to support a computer's participation in a cooperative dialogue.In this paper we introduce a formal theory of dialogue based in a model -P systems --already introduced in theoretical computer science, which should be easily implemented. Our aim is to introduce a theoretical model of conversation with the explicitness, formahty and efficiency that are required for computer implementation.The essential characteristic of the model is the use of a simple computational mechanism for the interaction between cellular membranes in order to generate a conversation structure. So, dialogue P systems can be placed in the line of those approaches to modelling conversation that use the so-called dialogue grammars, a useful computational tool to express simple regularities of dialogue behaviour.P systems -introduced in [10]-are models of computation inspired by some basic features of biological membranes. They can be viewed as a new paradigm Please use the foUmring format when citing this chapter: