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Discrete event simulations can be used to analyse natural and artificial phenomena. To this end, one provides models whose behaviours are characterized by discrete events in a discrete timeline. By running such a simulation, one can then observe its properties. This suggests the possibility of applying on-the-fly verification procedures during simulations. In this work we propose a method by which this can be accomplished. It consists in modelling the simulation as a a transition system (implicitly), and the property to be verified as another transition system (explicitly). The latter we call a simulation purpose and it is used both to verify the success of the property and to guide the simulation. Algorithmically, this corresponds to building a synchronous product of these two transitions systems on-the-fly and using it to operate a simulator. The precise nature of simulation purposes, as well as the corresponding verification algorithm, are largely determined by methodological considerations important for simulations.