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Multicast is an important application in all-optical WDM networks. The wavelength assignment problem for WDM multicast is to assign a set of wavelengths to the links of a given multicast tree. In an all-optical WDM network without wavelength conversions, wavelength assignment is the key to guarantee the quality of service and to reduce communication costs. In this paper, we study wavelength assignment for WDM multicast with two criteria, to cover the maximum number of destinations, and to minimize the wavelength costs. The computational complexity of the problem is studied. Three heuristic algorithms are proposed and the worst-case approximation ratios for some heuristic algorithms are given. We also derive a lower bound of the minimum total wavelength cost and an upper bound of the maximum number of reached destinations. The efficiency of the proposed heuristic algorithms and the effectiveness of the derived bounds are verified by the simulation results.