We study genetic algorithms (GAs)-based identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network models and radial basis function network models. Under perfect state measurements, we first show that a standard GA-based estimation scheme, in its full potential, even though leading to a satisfactory model for state estimation, may generally not yield a sufficiently accurate system model, i.e. the parameter estimates do not secure a good approximant for the system nonlinearity. We then introduce a new approach that utilizes a robust identification scheme, which leads to a good approximation of the nonlinearity in the system. Several numerical and simulation studies included in the paper demonstrate the effective use of GAs in this framework, in searching for the parameter values that lead to the "best" finite-dimensional approximation of the nonlinearities in the system dynamics.