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Many control texts do not provide an adequate insight into the assumptions inherent in the describing function technique for analyzing the stability of nonlinear systems. A laboratory experiment is described which provides this background by investigating the harmonic content of the signals in an analog simulation of a third-order system which incorporates an ideal relay. The paper then proceeds to show how the simulation may be extended to investigate the stability of the system when the relay includes a dead zone or hysteresis. It is shown that under these favorable con ditions, the describing function gives good agreement with the results of the simulation.