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This paper focuses on the development of adaptive fuzzy neural network control (AFNNC), including indirect and direct frameworks for an n-link robot manipulator, to achieve high-precision position tracking. In general, it is difficult to adopt a model-based design to achieve this control objective due to the uncertainties in practical applications, such as friction forces, external disturbances, and parameter variations. In order to cope with this problem, an indirect AFNNC (IAFNNC) scheme and a direct AFNNC (DAFNNC) strategy are investigated without the requirement of prior system information. In these model-free control topologies, a continuous-time Takagi-Sugeno (T-S) dynamic fuzzy model with online learning ability is constructed to represent the system dynamics of an n-link robot manipulator. In the IAFNNC, an FNN estimator is designed to tune the nonlinear dynamic function vector in fuzzy local models, and then, the estimative vector is used to indirectly develop a stable IAFNNC law. In the DAFNNC, an FNN controller is directly designed to imitate a predetermined model-based stabilizing control law, and then, the stable control performance can be achieved by only using joint position information. All the IAFNNC and DAFNNC laws and the corresponding adaptive tuning algorithms for FNN weights are established in the sense of Lyapunov stability analyses to ensure the stable control performance. Numerical simulations and experimental results of a two-link robot manipulator actuated by dc servomotors are given to verify the effectiveness and robustness of the proposed methodologies. In addition, the superiority of the proposed control schemes is indicated in comparison with proportional-differential control, fuzzy-model-based control, T-S-type FNN control, and robust neural fuzzy network control systems.