Abstarct: The adaptive control problem for singular systems is investigated in this thesis. Singular systems (a.k.a, descxriptor systems and differential-algebraic systems) which contain both differential and algebraic equations have attracted a lot of research interest in recent years. This kind of models is a natural and convenient representation of real systems and can deal with complex and constrained systems more easily. Many applications of singular systems have been discussed in different systems such as circuit systems, power systems, economic systems, constrained robots, chemical process and biological systems. Several control methods are therefore rapidly extended for singular systems. However, the complex nature of this class of systems causes some difficulties in control approaches. In addition to being stable, an acceptable singular system should be regular and impulse free. A system which poses these three characteristics is known as an admissible system. The control objective is therefore making the system admissible. In this thesis, firstly, a short discussion on singular systems characteristics and formulation is provided, and the theories and assumptions used for control design are presented. Afterwards, an adaptive state feedback control approach for a one-input linear singular system is investigated which makes the closed loop dynamics of this class of systems regular, impulse free and stable. The proposed adaptive method is baxsed on the Lyapunov theorem to ensure the admissibility of the descxriptor system. Then the presented method is extended to a state tracking controller for multi input linear singular systems. We then prove that by some small changes in adaption law, the proposed control method can be used for nonlinear singular systems in which the nonlinear part satisfies the Lipschitz condition. The presented controller is fairly simple compared to the existing methods in the literature proposed for the control problem of singular systems. At the end, an adaptive model reference control approach is designed for nonlinear singular systems. All of the nonlinear systems in this thesis are assumed to be affine ones. For better illustration of the proposed controllers, some simulations have been done, and the results emphasize the effectiveness of the presented methods.