This paper presents a sequential identification scheme for continuous nonlinear dynamical systems using neural networks. The nonlinearities of the dynamical systems are assumed to be unknown. The identification model is a gaussian radial basis function neural network that grows gradually to span the appropriate state space and of sufficient complexity to provide an approximation to the dynamical system. The sequential identification algorithm for continuous dynamical nonlinear systems is developed in the continuous-time framework instead of in discrete time. The approach, different from the conventional methods of optimizing a cost function, attempts to ensure stability of the overall system while the neural network learns the system dynamics. The stability and convergence of the overall identification scheme are guaranteed by parameter adjustment laws developed using the Lyapunov synthesis approach. To ensure that the modelling error can be reduced arbitrarily, a one-to-one mapping is proposed so that the states and inputs of the system are transferred into compact sets. The operation of the sequential identification scheme is illustrated using simulated experimental results.