This paper is devoted to state and parameter estimation for a large class of nonlinear systems using a radial basis function neural network predictor in the continuous time domain. The proof of the convergence of the estimates to their true values is achieved using Lyapunov theories and does not require the classical persistent excitation condition to be satisfied by the input signal. Comparisons between the results obtained and those of the method based on the sliding mode observer are also presented in the case of the estimation of the synchronous machine inductance parameters. The performance exhibited by the obtained results demonstrate that the proposed scheme can also work very well if the stator resistance varies due to the stator winding heating. The comparative results show globally that the proposed algorithm gives better performance than the method based on the sliding mode observer in terms of the convergence rate and the state/parameter accuracies.