In this paper, we study the identification of two challenging benchmark problems using neural networks. Two different global optimization approaches are used to train a recurrent neural network to identify two challenging nonlinear models, the cascaded tanks, and the Bouc-Wen system. The first approach, quotient gradient system (QGS), uses the trajectories of the nonlinear dynamical system to find the local minima of the optimization problem. The second approach, dynamical trajectory-based methodology, uses two different nonlinear dynamical systems to find the connected components of the feasible region and then searches the regions for local minima of the optimization problem. Simulation results show that both approaches effectively identify the model of the cascade tanks and the Bouc-Wen model.