This work considers the problem of identifying the fault in a faulty dynamical system on the basis of the system's input and output signals only. For this purpose, a model-based method for the design of diagnostic tests which consist of specific input signals and appropriate residual generators is developed. The method extends the structure graph of dynamical systems in order to represent the couplings in a system which has been brought to a specific operating region. The resulting local structure graph is used to determine specific residual generators which can distinguish between faults on the basis of the system's input and output signals in the corresponding operating region. Algorithms to determine advantageous operating regions and input signals which drive the system into such operating regions are given. The application of the method to determine diagnostic tests is demonstrated using a typical automotive system, a throttle valve.