Dynamics analysis studies of spiking neural network behavior entails the computation of a large number of simulation scenarios. Moreover, when the simulated neural microcircuits are fairly large, the use of multiple cores in a simulation tends to be beneficial. In this paper we focus on the parallelization of an asynchronous simulation strategy with OpenMP threads and on the management of the neural simulations on compute grids. The first results show a parallel efficiency in the ranges of 0.31 -0.98, with hyper-threading disabled or enabled, resp. By using the grid as underlying middleware for performing the simulations, we could generate and manage hundreds of simulation scenarios in an easy way.