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This paper presents an approximate analysis of oscillating servo systems with random inputs. The power spectrum relations for these systems are established by extending the dual-input describing function method. The analysis shows that the system exhibits a quasi-linear mode of operation similar to that previously shown to exist for a sinusoidal input. Distortion components resulting from the closed loop system are examined, and conditions for quasi-linear operation (small distortion) are given in terms of signal level and bandwidth. Some analog computer results are presented to demonstrate the applicability of the quasi-linear theory to the random input case.