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A restoration mechanism based on backup capacity provides a solution for assuring network survivability. In this paper we propose an adaptive survivability admission control mechanism using backup virtual paths for self-healing asynchronous transfer mode (ATM) networks. Working virtual paths (WVP) and backup virtual paths (BVP) are configured during the network design phase. For each call request, the proposed mechanism selects a pair of WVP and BVP followed by bandwidth reservation for the pair only if both the WVP and the BVP selected succeed in the call admission control. A backup dependency matrix (BDM) is suggested for recording the most up-to-date information of backup capacity required on a link for restoring a failure on other links. However backup capacity actually reserved on a link is shared by all BVP passing the same link. This "sharing" concept substantially reduces the amount of backup capacity required. The selection of BVP uses the BDM so as to make the selection adaptive to the current traffic loads on the network. Two BVP selection methods, min-cost and min-expectation, are proposed. The min-cost strategy increases network utilization while maintaining full survivability under a single link failure. On the contrary, the min-expectation strategy enhances network survivability by slightly reducing network utilization.