The utilization of Genetic Algorithms (GA)in the development of Artificial Neural Networks is a very active area of investigation. The works that are being carried out at present not only focus on the adjustment of the weights of the connections, but also they tend, more and more, to the development of systems wich realize task of design and training, in parallel. To cover these necessities and, as an open platform for new developments, in this article it is shown a multilevel GA architecture wich establishes a difference between the design and training tasks. In this system, the design tasks are preformed in a parallel way, by using different machines. Each design process has associated a training process as an evaluation function. Every design GA interchanges solutions in such a way that they help one each other towards the best solution working in a cooperative way during the simulation.