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This paper develops novel mechanisms for recovering from failures in IP networks with proactive backup path calculations and Internet Protocol (IP) tunneling. The primary scheme provides resilience for up to two link failures along a path. The highlight of the developed routing approach is that a node reroutes a packet around the failed link without the knowledge of the second link failure. The proposed technique requires three protection addresses for every node, in addition to the normal address. Associated with every protection address of a node is a protection graph. Each link connected to the node is removed in at least one of the protection graphs, and every protection graph is guaranteed to be two-edge-connected. The network recovers from the first failure by tunneling the packet to the next-hop node using one of the protection addresses of the next-hop node; the packet is routed over the protection graph corresponding to that protection address. We prove that it is sufficient to provide up to three protection addresses per node to tolerate any arbitrary two link failures in a three-edge-connected graph. An extension to the basic scheme provides recovery from single-node failures in the network. It involves identification of the failed node in the packet path and then routing the packet to the destination along an alternate path not containing the failed node. The effectiveness of the proposed techniques were evaluated by simulating the developed algorithms over several network topologies.