Space and time are key variables for identifying patterns in sports contests. In this article, the spatial-temporal interactions between players are considered in terms of a dynamical system. In this view, the dynamical interactions among players are hypothesized to give rise to the behavioural patterns that appear to characterize various types of sports contests. While these patterns often seem open to visual detection, a formal description of these patterns remains equivocal. This article will serve as a platform upon which such a lawful description might be based. With this in mind, the language of dynamical systems was suggested as offering a suitable basis upon which to investigate sports behaviours (McGarry et al., 2002). (See McGarry and Franks, 1996, and McGarry et al., 1999, for earlier work that led to forwarding this consideration.) The general absence of research studies in this area of sports inquiry reflects the newness of this type of approach for sports analysis. For this reason, this article first presents some examples on the dynamical features of sports behaviours from extant data recorded on squash contests. The view of sports contests as a dynamical system is later extended from one-vs-one interactions to many-vs-many interactions, with specific references to soccer. The ideas presented in this article expand upon those reported in McGarry et al. (2002).