The paper concerns the model-based diagnosis of continuous-variable systems whose state can only be measured through a quantizer. The diagnosis is based on the investigation whether the observed discrete input and output sequences are consistent with a discrete-event model of the quantized system. The paper describes a necessary and sufficient condition for the discrete-event model to be suitable for diagnosis. This condition is independent of the specific model form and of the diagnostic algorithm applied to the model. Within a hierarchy of models with increasing accuracy ail of which satisfy this modelling requirement the quality of the diagnostic result increases. The results are illustrated by an example.