This paper deals with fault detection and identifcation in dynamic systems when the system dynamics can be modeled by smooth nonlinear diferential equations including afne, bilinear or linear parameter varying (LPV) systems. Two basic approaches will be considered, these apply diferential algebraic and diferential geometric tools. In the diferential algebraic approach the state elimination methods will be used to derive nonlinear parity relations. In the specifc case when a reconstruction of the fault signal is needed the dynamic inversion based approach will be investigated. This approach will also be studied from geometric point of view. The geometric approach, as proposed by Isidori and De Persis, is suitable to extend the detection flter and unknown input observer design approaches (well elaborated for LTI systems) to afne nonlinear systems. Beyond the development of the theory of fault detection and identifcation it is equally important to ofer computable methods and to analyze the robustness properties against uncertainties. Both the observer based and the inversion based approaches will be elaborated for LPV systems that may ofer computational tools inherited from linear systems and also allows to design for robustness utilizing results from H∞ robust fltering and disturbance attenuation.