Design of control techniques nonlinear systems, where state measurement is not available, still poses a major challenge. Recent successful applications of static neural networks for control suggest that certain intrinsic properties of neural networks could also be utilised for output feedback control, where the neural network serves as a dynamic model of the system. Some steps have been taken in this direction, most of them of a heuristic nature. An adaptive control technique for nonlinear plants with an unmeasurable state is presented based on a recurrent neural network employed as a dynamical model of the plant. Using this dynamical model a feedback linearising control is computed and applied to the plant, while parameters of the model are updated online to allow for partially unknown and time-varying plant. Stability of the algorithm is proved for the case of constant reference output, and some further insights into convergence issues for the general case of tracking problem are provided. Performance of the proposed control method is illustrated in simulations.