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This study presents a protective algorithm for discrimination and classification of short-circuit faults on parallel circuit transmission lines. The proposed algorithm is composed of two stages. In the first stage, the cross-differential technique is employed to identify close-in internal faults. The second stage is assigned to discriminate remote faults occurring at the end part of the protected transmission line. This stage is based on the travelling waves generated by the open switching of the transmission line circuit breakers. Using these travelling waves, the algorithm can quickly identify operation of remote end circuit breakers and discriminate between internal and external faults. The proposed algorithm also classifies the faulted phases. Moreover, it covers inter-circuit faults, in which phases of both parallel circuits get involved in the fault. Extensive simulation studies were performed to evaluate the proposed algorithm performance. It is concluded that this algorithm provides a fast and reliable scheme for protection of parallel transmission lines.