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We study constrained multicast in WDM networks under multi-drop model. Under this model to route a given multicast connection is to produce a set of light-trees rooted at the source such that at most k destinations are designated in each light-tree where the data drops and every destination must receive the data in such a way. The cost of routing is the total costs of light-trees constructed. To allocate wavelengths to the multicast connection Is to assign a wavelength to each light-tree in such a way that two light-trees must be assigned different wavelengths if they share a common, fiber link. In the paper we first prove that the problem of finding the multi-drop routing of minimal cost Is polynomial-time solvable for k=2 and NP-hard for k>2. We then propose some routing algorithms with guaranteed constant approximation performance ratios. Our simulation study shows that compared with point-to-point connection multi-drop routing can significantly save not only the network cost but also wavelengths, and when k≥5 its performance is very close to the performance of unconstrained multicast.