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Part I contains an evaluation of a proposal by O. J. M. Smith on the control, by Wiener prediction and a non-linear combination of input and feedback signals, of a saturating element driving a primarily inertial load. This evaluation consists of simulation tests on a high-speed analog computer with actual continuous random Gaussian inputs. Results presented include: (1) Variation of the mean squared error with prediction time; (2) Optimum, system parameter dependence upon input signal level; (3) For fixed saturating level, mean squared error comparisons between the predictor-relay servo, and the "McDonald" and "optimum relay" servo; (4) Effects of different input spectral width and location; and (5) Data on a variation of the basic predictor-relay servo, where minimal-error parameters become relatively independent of input signal level. Part II is concerned with the error signal. The character of the error is discussed by examples from sinusoidal, transient, and random inputs. In an extension of a paper by K. Chuang and L. F. Kazda, the error probability density and distribution functions are found analytically, the results being valid for a class of compensated relay servos. The main result is that the large-amplitude error probability density is of a single-exponential form. Analog computer measurement of the error probability distribution function verifies the theory.