Advancing over simple threshold checking, modern fault diagnosis approaches utilize many different methods for signal processing, supervision and classification tasks. This contribution presents a residual-based approach for fault detection and diagnosis for nonlinear processes. It is an extension of well-known methods for a certain type of "grey-box" models. These models are able to approximate nonlinear processes and can be trained from measurement data. The resulting residuals form a basis for a new, self-learning diagnosis scheme in order to isolate different fault situations. The applicability of the methods is shown for the fault detection and diagnosis of a thermal pilot plant.