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A theory for the diagnosabilty of nonlinear dc circuits (memoryless systems) is developed. Based on an input-output model, a necessary and sufficient condition for the local diagnosability of the system, which is a rank test on a matrix, is derived. Various ways of reducing the computational complexity of this test are indicated. A sufficient condition for single fault diagnosability, which is much weaker than the necessary and sufficient condition for local diagnosability, is also derived. It is also shown that for diagnosable systems, it is possible to to pick a finite number of test inputs that are sufficient to diagnose the system. An illustrative example is presented.