A second link in a network is reconfigured after failure of a first link, so that multiple-link failures may be survived. After receipt of an OSPF link state advertisement (LSA) indicating use of a backup path bl after the failure of link l, new backup paths are determined for each impacted link (x,y) that has a backup path sharing one or more links with the backup path bl. The new backup paths are computed while ignoring the failed link l, the impacted link (x,y), and links common to the backup paths b(x,y) and bl. The LSA protocol is modified to accommodate information used in determining whether a link is an impacted link.