A signalling network is a network of reactions that govern how a cell responds to its environment. A pathway is a dynamic flow of "signal" through the network (signal transduction), for example from a receptor to a transcription factor that enables expression of a gene. In this paper we introduce a method to compute all pathways in a signalling network that satisfy a simple property constraining initial, final and intermediate states. This method, concerned with signal transduction, is compared to the steady state view underlying Petri net place/transition invariants and flux balance analysis. We apply the method to the signalling network model being developed in the Pathway Logic project and identify knockout/inhibition targets and common (pathway) events. This approach also allows us to better understand and formalise the interaction between pathways in a network, for example to identifying pathway inhibition targets that limit the effect on unrelated pathways.