This dissertation addresses fault detection and isolation (FDI) for nonlinear systems based on models using two different approaches. The first approach detects and isolates single and multiple faults, particularly when there are restrictions in measuring process variables. The FDI model-based method is based on nonlinear state estimators, in which the estimates are calculated under high filtering, and a high fidelity residuals model, obtained from the difference between measurements and estimates. In the second approach, a robust fault detection and isolation (RFDI) system, that handles both parameter estimation and parameters with uncertainties, is proposed in which complex models can be simplified with nonlinear functions so that they can be formulated as differential algebraic equations (DAE). In utilizing this framework, faults are identified by performing a statistical analysis. Finally, comparisons with existing data-driven approaches show that the proposed model-based methods are capable of distinguishing a fault from the diverse array of possible faults, a common occurrence in complex processes. / text