In this paper fault diagnosis is studied for linear time varying descriptor systems, which are the discrete time counterpart of the continuous time dynamic systems described by differential-algebraic equations. This class of systems includes and is broader than the well-known state space systems. The framework of descriptor systems is particularly useful for studying dynamic systems exhibiting time varying singularities. Actuator faults and sensor faults are respectively modeled as parametric changes in the state equation and in the output equation. The main result of this paper consists in extending an adaptive observer, initially designed for state space systems, to descriptor systems. Based on this result, fault diagnosis is performed by estimating the parameters characterizing actuator and sensor faults.