The design and analysis of fault diagnosis architectures using the model-based analytical redundancy approach has received considerable attention during the last two decades. One of the key issues in the design of such fault diagnosis schemes is the effect of modelling uncertainties on their performance. This paper describes a fault diagnosis algorithm for a class of nonlinear dynamic systems with modelling uncertainties when not all states of the system are measurable. The main idea behind this approach is to monitor the plant for any off-nominal system behaviour due to faults utilizing a nonlinear online approximator with adjustable parameters. The online approximator only uses the system input and output measurements. A nonlinear estimation model and learning algorithm are described so that the online approximator provides an estimate of the fault. The robustness, sensitivity, stability and performance properties of the nonlinear fault diagnosis scheme are rigorously established under certain assumptions on the failure type. A simulation example of a simple second-order system is used to illustrate the robust nonlinear fault diagnosis scheme.