Standard grammar formalisms are defined without reflection of the incremental, serial and context-dependent nature of language processing; any incrementality must therefore be reflected by independently defined parsing and/or generation techniques, and context-dependence by separate pragmatic modules. This leads to a poor setup for modelling dialogue, with its rich speaker-hearer interaction and high proportion of contextdependent and apparently grammatically ill-formed utterances. Instead, this paper takes an inherently incremental grammar formalism, Dynamic Syntax (DS) , proposes a context-based extension and defines corresponding context-dependent parsing and generation models together with a resulting natural definition of context-dependent well-formedness. These are shown to allow a straightforward model of otherwise problematic dialogue phenomena such as shared utterances, ellipsis and alignment. We conclude that language competence is a capacity for dialogue.