— Networks employ link protection to achieve fast recovery from link failures. While the first link failure can be protected using link protection, there are several alternatives for protecting against the second failure. This paper formally classifies the approaches to dual-link failure resiliency. One of the strategies to recover from dual-link failures is to employ link protection for the two failed links independently, which requires that two links may not use each other in their backup paths if they may fail simultaneously. Such a requirement is referred to as Backup Link Mutual Exclusion (BLME) constraint and the problem of identifying a backup path for every link that satisfies the above requirement is referred to as the BLME problem. This paper develops the necessary theory to establish the sufficient conditions for existence of a solution to the BLME problem. Solution methodologies for the BLME problem is developed using two approaches by: (1) formulating the backup path...