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Anycasting has recently become an important research topic, especially for replicated servers. With anycasting, applications can request the "nearest" server for provision of desired (multimedia) service. In this paper, we study efficient distributed admission control (DAC) for anycast flows. We focus on algorithms that perform destination selection and efficient path establishment. Taking advantage of anycasting, our distributed algorithms differ from each other in their dependence on system status information. Performance data obtained through mathematical analysis and simulations show that, in terms of admission probabilities, DAC systems that are based on local status information have performance levels close to those that utilize global and dynamic status information. This renders our DAC algorithms useful not only for the network layer, but also for the application layer admission control for anycast flows.