A previous paper outlined the principles of a new method for dynamically varying the shape of polarised quadrilateral relay characteristics for the protection of e.h.v. transmission lines. The present paper extends these methods to the protection of double-circuit lines. Consideration is given to the compensation of earth-fault relays, and it is shown that compensation schemes which ignore the effect of mutual coupling between circuits are desirable. Digital-computer application studies of a typical double-circuit 400kV transmission line of earthed construction indicate that, from the point of view of accuracy and fault coverage, there is little advantage in the use of variable devices in zone 1. However, they enable a greater proportion of the protected feeder to be covered with minimum fault-detection time. Emphasis is placed on the response of relays connected to healthy conductors, and the possibility of avoiding unwanted tripping emerges. A high degree of immunity to maloperation during heavy-circuit loading and power swings is achieved.