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This paper aims to establish the theoretical and experimental validity of the two degrees of freedom adaptive tracking control of a nonlinear system. This architecture is based on an adaptive feedforward control via the internal inverse model of the controlled object. In this paper, we consider two different approaches to construct such a inverse model, which are the feedback error learning (FEL) methods and the just-in-time (JIT) methods. For a typical nonlinear controlled object, a two-links direct drive (DD) arm, a stability and a convergence of the adaptive control system are proven theoretically, numerically and experimentally. For the DD arm in the time delay free case, it is shown that both FEL and JIT architectures achieved superior tracking performances for a circle target. These results suggest the possibility of applying the two degrees of freedom adaptive control systems in this paper to more complicated nonlinear control systems.