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In this paper we present a novel performance analysis technique for large scale systems modelled in the stochastic process algebra PEPA. In contrast to the well-known approach of analysing via continuous time Markov chains, our underlying mathematical representation is a set of coupled ordinary differential equations (ODEs). This analysis process supports all of the comhinators of the PEPA algebra and is well suited to systems with large numbers of replicated components. The paper presents an elegant procedure for the generation of the ODEs and compares the results of this analysis with more conventional methods.