Abstract. Given the combinatorial nature of cellular signalling pathways, where biological agents can bind and modify each other in a large number of ways, concurrent or agent-based languages seem particularly suitable for their representation and simulation [1,2,3,4]. Graphical modelling languages such as [5, 6, 7, 8], or the closely related BNG language [9,10,11,12,13,14], seem to afford particular ease of expression. It is unclear however how such models can be implemented.1 Even a simple model of the EGF receptor signalling network can generate more than 1023 non-isomorphic species [5], and therefore no approach to simulation based on enumerating species (beforehand, or even on-the-fly) can handle such models without sampling down the number of potential generated species. We present in this paper a radically different method which does not attempt to count species. The proposed algorothm uses a representation of the system together with a super-approximation of its `event horizon...