The increased requirements to high-speed travelling-wave relay protective systems of high- and extra-high-voltage transmission lines are imposed for ensuring high reliability of interaction of protection algorithms and fault-phase selection detectors of single-phase automatic reclosings for the purpose of ensuring the necessary conditions for the maximum use of advantages of these protective systems. The discussion covers travelling-wave relay protection device operation principles, together with the fault-phase selection detector, in which the comparison of magnitudes of phase fault currents (voltages) of the transmission lines average in absolute values takes place. Criteria for selecting the response and return time of the travelling-wave protection directional elements and the fault-phase selection detectors are developed that allow improving the efficiency of operation of protection in the single-phase automatic reclosing cycle. It is shown that the response times of the fault-phase selection detector and the directional elements should be commensurate and the devices themselves should have the ability to detect not only the occurrence of a short circuit, but also the short circuit’s transition to more complex modes in the single-phase automatic reclosing cycle. In the open-phase mode of transmission line operation, the reset time of protection can be significantly reduced compared to the previously selected values due to the fact that the decay constants of the free periodic component are 30–50 ms and decrease with the component frequency and increase in transient resistance at the point of a short circuit.