The use of sliding mode observers as a model-based method is proposed for robust fault detection and isolation in linear and nonlinear nuclear systems. A sliding mode output observer and a sliding mode state observer are designed and applied to a U-tube steam generator model, a coupled nonlinear reactor model, and a pressurizer model to detect additive and multiplicative faults in the presence of uncertainties and measurement noise. Numerical results for both steady-state and transient responses of the example systems are presented to illustrate the effectiveness of the proposed method.