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In this paper, we address the problems of constructing both source-based and core-based many-to-many multicast trees for applications with delay and/or delay jitter constraints. We use the source-destination delay bound and the interdestination delay fitter bound as the QoS requirement and formulate the delay and delay jitter constrained many-to-many multicast tree (D2M3T) problems. For the source-based, many-to-many multicast paradigm, we extend an existing scheme that builds a one-to-many, QoS-compliant multicast tree and devise a solution scheme that first finds a feasible multicast tree for each source node in the multicast group and then a minimum cover of these multicast trees such that there exists at least one feasible multicast tree in the minimum cover for each source node. For the core-based, many-to-many multicast paradigm, we first derive a necessary and sufficient condition for a core-based multicast tree to be feasible and then devise a solution scheme based on the condition derived. We validate and evaluate both proposed schemes via simulations.