This paper focuses on residual generation for model-based fault diagnosis. Specifically, a methodology to derive residual generators when nonlinear equations are present in the model is developed. A main result is the characterization of computation sequences that are particularly easy to implement as residual generators and that take causal information into account. An efficient algorithm, based on the model structure only, which finds all such computation sequences, is derived. Furthermore, fault detectability and isolability performances depend on the sensor configuration. Therefore, another contribution is an algorithm, also based on the model structure, that places sensors with respect to the class of residual generators that take causal information into account. The algorithms are evaluated on a complex highly nonlinear model of a fuel cell stack system. A number of residual generators that are, by construction, easy to implement are computed and provide full diagnosability performance predicted by the model.