Standard grammar formalisms are defined without reflection of the incremental and serial nature of language processing, and incrementality must therefore be reflected by independently defined parsing and/or generation techniques. We argue that this leads to a poor setup for modelling dialogue, with its rich speaker-hearer interaction, and instead propose context-based parsing and generation models defined in terms of an inherently incremental grammar formalism (Dynamic Syntax), which allow a straightforward model of otherwise problematic dialogue phenomena such as shared utterances, ellipsis and alignment.Article