The two principal areas of natural language processing research in pragmatics are belief modelling and speech act processing. Belief modelling is the development of techniques to represent the mental attitudes of a dialogue participant. The latter approach, speech act processing, based on speech act theory, involves viewing dialogue in planning terms. Utterances in a dialogue are modelled as steps in a plan where understanding an utterance involves deriving the complete plan a speaker is attempting to achieve. However, previous speech act based approaches have been limited by a reliance upon relatively simplistic belief modelling techniques and their relationship to planning and plan recognition. In particular, such techniques assume precomputed nested belief structures. In this paper, we will present an approach to speech act processing based on novel belief modelling techniques where nested beliefs are propagated on demand.