1. INTRODUCTION Dynamics is the formal study of systems involving states and transitions between states. A natural application of dynamics is to the study of language processing, where words or morphemes can be thought of as actions which perform transitions between states of the language processor. The paper concentrates on sentence as opposed to text processing, and shows how dynamics can lead to novel parsing algorithms and to new possibilities for the formal description of syntactic constructions, in particular, for the description of non-constituent coordination. The use of dynamics in algorithm development will be illustrated by presenting a particular parsing algorithm which was developed for a 'core' lexicalised grammar, Lexicalised Dependency Grammar (Milward 1992) which resembles both simplified HPSG (Pollard and Sag 1993) and dependency grammar as formalised by Gaifman (see Hays 1964). The algorithm is fully incremental, providing a semantic representation word by word. It also exhibits reduced non-determinism relative to other almost-incremental algorithms 1 by using types instead of partial parse trees. These can be packed further using graph structuring (cf. Tomita 1985). Although dynamics specifies the states of a process and the possible mappings between states, it does not specify the control strategy (how the state space is traversed). Suitable languages for dynamics are thus both formal and declarative, and can be used to express linguistic generalisations. The final part of the paper regards the dynamics provided for the core lexicalised grammar as a grammar in its own right, Dynamic