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In this paper, we investigate approaches and algorithms for establishing a multicast session in a mesh network while protecting the session against any single link failure, e.g., a fiber cut in an optical network. First, we study these approaches and algorithms to protect a single multicast tree in a mesh network and then extend it to dynamically provision survivable multicast connections (where connections come and go) in an optical wavelength-division multiplexing (WDM) network. We propose two new and efficient approaches for protecting a multicast session: 1) segment protection in which we protect each segment in the primary tree separately (rather than the entire tree) and allow these backup segments to share edges with the other existing primary and backup segments and 2) the path-pair protection in which we find a path-pair (disjoint primary and backup paths) to each destination and allow a new path pair to share edges with already-found path pairs. Unlike previous schemes, such as finding link-disjoint trees and arc-disjoint trees, our new schemes 1) guarantee a solution where previous schemes fail and 2) find an efficient solution requiring less network resources. We study these approaches and algorithms systematically, starting with the existing approaches such as fully link-disjoint and arc-disjoint trees and then presenting our new and efficient proposed approaches, such as segment-disjoint and path-disjoint schemes for protecting multicast connections. Our most efficient algorithm, based on the path-pair protection scheme, called optimal path-pair-based shared disjoint paths (OPP-SDP) algorithm, finds a solution if such a solution exists and outperforms all the other schemes in terms of network cost. We also show that OPP-SDP performs close to the optimal solution obtained by solving a mathematical formulation of the problem expressed as an integer linear program. Building upon the study on protecting a single tree, we perform simulations, employing the above protection schemes, to study dynamic provisioning of survivable multicast sessions (where sessions come and go) in a WDM mesh network. Our simulations show that the most efficient scheme, OPP-SDP, has minimum blocking probability.