An adaptive observer for a class of single-input single-output (SISO) nonlinear systems is proposed using a generalized dynamic recurrent neural network (DRNN). The neural-network (NN) weights are tuned on-line, with no off-line learning required. No exact knowledge of nonlinearities in the observed system is required. Furthermore, no linearity with respect to unknown system parameters is assumed. The DRNN observer does not assume that nonlinearities in the system are restricted to the system output only. The overall adaptive observer scheme is shown to be uniformly ultimately bounded. Simulation results have verified the performance of the DRNN observer.