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This paper addresses the problem of dynamically provisioning both low-speed unicast and multicast connection requests in mesh-based wavelength division multiplexing (WDM) optical networks. Several routing/provisioning schemes to dynamically provision both unicast and multicast connection requests are presented. In addition, a constraint-based grooming strategy is devised to utilize the overall network resources as efficiently as possible. Based on this strategy, several different sequential multicast grooming heuristics are first presented. Then, we devise a hybrid grooming approach and combine it with sequential approaches to achieve a grooming scheme that is biased toward serving multicast traffic demands in comparison with all other sequential grooming approaches. To achieve our objective, we decompose the problem into four subproblems: 1) routing problem; 2) light-tree-based logical-topology-design problem; 3) provisioning problem; and 4) traffic-grooming problem. The simulation results of the proposed schemes are compared with each other and with those of conventional nongrooming approaches. To the best of our knowledge, this is the first detailed paper to address and examine the problem of grooming dynamic multicast traffic demands.