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Currently, many bandwidth-intensive applications require multicast services for efficiency purposes. In particular, as wavelength division multiplexing (WDM) technique emerges as a promising solution to meet the rapidly growing demands on bandwidth in present communication networks, supporting multicast at the WDM layer becomes an important yet challenging issue. In this paper, we introduce a systematic approach to analyzing the multicast connection capacity of WDM switching networks with limited wavelength conversion. We focus on the practical all-optical limited wavelength conversion with a small conversion degree d (e.g., d=2 or 3), where an incoming wavelength can be switched to one of the d outgoing wavelengths. We then compare the multicast performance of the network with limited wavelength conversion to that of no wavelength conversion and full wavelength conversion. Our results demonstrate that limited wavelength conversion with small conversion degrees provides a considerable fraction of the performance improvement obtained by full wavelength conversion over no wavelength conversion. We also present an economical multistage switching architecture for limited wavelength conversion. Our results indicate that the multistage switching architecture along with limited wavelength conversion of small degrees is a cost-effective design for WDM multicast switching networks.