A known approach to the analysis of stochastic relay control systems involves replacing the relay by a correlation-transforming device. The accuracy of this technique is investigated in the present paper. Differential equations are obtained for system autocorrelation functions, and are solved either analytically or computationally. It is found that the approach gives less accurate results than Booton's statistical linearization procedure. In Part I a first-order relay control system with a white noise disturbance was considered. In Part II the treatment is applied to a second-order system.