This paper covers the state of the art in nonlinear dynamical system identification using Artificial Neural Networks (ANN). The main approaches in the last two decades are presented in unified framework. ANN have unique characteristics, which enable them to model nonlinear dynamical systems. The main problems with the choice of ANN model structure are considered and commonly used identification schemes are proposed. A procedure for derivation of parameter estimation law using Lyapunov synthesis approach, which guarantees stability and convergence of the overall identification scheme, is presented.