Abstarct: This dissertation deals with adaptive fuzzy control for a class of nonlinear descxriptor systems. Descxriptor systems refer to systems with both dynamic (differential) and static (algebraic) equations. In nonlinear control theory, an important approach is adaptive fuzzy control of uncertain nonlinear systems which should be extended to nonlinear descxriptor systems. Adaptive controllers can be classified into two categories, i.e. direct and indirect ones. One section of this thesis is about direct adaptive fuzzy control for uncertain affine nonlinear descxriptor systems. Two cases are considered: in the first one it is assumed that the control gain is known while in the second one it is an unknown-but-bounded symmetric positive definite matrix. To account for uncertainties in the system dynamics, a fuzzy system is employed to directly approximate the unknown ideal controller. The adjustable parameters of the fuzzy system are updated by either a Lyapunov-baxsed adaptative law in the first case, or a gradient descent algorithm minimizing a suitable quadratic cost function in the second case. Furthermore, an auxiliary compensating signal is designed to guarantee that the tracking error asymptotically vanishes in both cases. Another section focuses on indirect adaptive fuzzy control of nonlinear descxriptor systems aiming to guarantee asymptotic tracking of a regular and impulse-free descxriptor reference model. The proposed controller exploits the universal approximation capability of Takagi-Sugeno-Kang (TSK) fuzzy models for the identification of the unknown system dynamics. In the proposed method, the asymptotic tracking of the reference model is guaranteed by suitable adaptation laws for the parameters of the TSK fuzzy model. Simulation results show how the proposed methods exhibit satisfactory performance thus demonstrating their effectiveness.