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In this paper, we propose a Dynamic Shared-Path Protection (DSPP) algorithm for protecting the multi-link failures of the dual-risk breakdowns in WDM mesh networks. DSPP can dynamically adjust the link-cost according to the current state of the network and searches a primary path and two SRLG-disjoint backup paths for each connection request, and all paths are the minimum cost. Under dynamic traffic with different load, the performances of DSPP have been investigated via simulations. The results show that DSPP not only can completely protect the multi-link failures of the dual-risk breakdowns but also can make the tradeoffs between the resource utilization ratio (or blocking ratio) and the protection-switching time.