The paper presents a method for identifying nonlinear systems using neural networks. It introduces a new parameter estimation algorithm based on the prediction error principle for neural networks with a single hidden layer. The approach is applied to both simulated and real data to demonstrate its effectiveness. The study shows that the classical back propagation algorithm is a special case of the new prediction error routines. Model validity tests are introduced to measure the quality of fit. The results indicate that neural networks can effectively model nonlinear systems. The paper also discusses the use of neural networks for system identification, including the development of both batch and recursive estimation algorithms. The neural network model is shown to be able to approximate any continuous function, making it a suitable tool for nonlinear system identification. The study includes simulation examples and real-world applications, demonstrating the effectiveness of the neural network approach in modeling nonlinear systems. The paper concludes that neural networks provide an effective method for identifying nonlinear systems and suggests further research in this area.The paper presents a method for identifying nonlinear systems using neural networks. It introduces a new parameter estimation algorithm based on the prediction error principle for neural networks with a single hidden layer. The approach is applied to both simulated and real data to demonstrate its effectiveness. The study shows that the classical back propagation algorithm is a special case of the new prediction error routines. Model validity tests are introduced to measure the quality of fit. The results indicate that neural networks can effectively model nonlinear systems. The paper also discusses the use of neural networks for system identification, including the development of both batch and recursive estimation algorithms. The neural network model is shown to be able to approximate any continuous function, making it a suitable tool for nonlinear system identification. The study includes simulation examples and real-world applications, demonstrating the effectiveness of the neural network approach in modeling nonlinear systems. The paper concludes that neural networks provide an effective method for identifying nonlinear systems and suggests further research in this area.