A third-order relay control system, controlled by means of the predictive strategies of Billingsley and Coales (1968), is studied. Expressions are given for a separatrix defined by the basic strategy, the switching surface defined by the modified strategy, and the settling time for a step response. The separatrix and some switching surfaces are represented by curves in a reduced state space. The results of the present paper were asserted, but not proved, in a previous paper.