The ramp response, sinusoidal response and random response of the discontinuous damping servome chanism devised by the author have been investigated by using a digital computer. In this servomechanism, the system damping ratio is changed from a small one to a large one by discontinuously switchi ng the relay according to the switching function which depends upon the error and the error rate, so as to make the response optimal for the step input. As its result, it has been revealed that, by modifying the switch ing function, this servomechanism has excellent response characteristics compared with those of the linear system.