In every network we see the link failures are common. For this purpose, we propose networks having the scheme to protect their links against the link failures. Networks use link protection to achieve fast recovery from link failures. While the first link failure can be protected using link protection (or defining back up node), there are several alternatives for protecting against the second failure. We formally classify the approaches to dual-link failure resiliency. One of the strategies to recover from dual-link failures is to employ link protection (or back) 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 due to finding new link the senders time is out and we have the problem of packet loss. In this we use Backup link mutual exclusion (BLME), when the links fail simultaneously. The solution methodologies for BLME problem is 1).for mulating the backup path selection as an integer linear program;2)developing a polynomial time heuristic based on minimum cost path routing.