We propose a novel modeling strategy for signals corrupted by additive noise. This combines a nonlinear parametric model to encapsulate domain knowledge, and a nonparametric component to extract further structure. Models of this type exploit the flexibility of nonparametric techniques without sacrificing physical interpretability. We propose a model building strategy based on Grey Box ideas [1] and show how our approach can be used to classify signals. To illustrate our approach we consider a radar target classification example.