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Our discussion in this article centers around various issues related to the use of anycasting in connection-oriented computer networks. Anycast is defined as a "one-to-one-of-many" transmission to deliver a packet to one of many hosts. Anycasting can be applied if the same content is replicated over many locations in the network. Examples of network techniques that apply anycasting are Content Delivery Networks (CDNs), Domain Name Service (DNS), Peer-to-Peer (P2P) systems ; The role of anycasting is growing concurrently with the popularity of electronic music, movies, and other content required by Internet users. In this work we focus on the optimization of anycast flows in connection-oriented networks. We formulate a model of anycast connections and next propose a heuristic algorithm based on the Lagrangean relaxation aimed to optimize jointly routes for anycast and unicast connections. Results of numerical experiments are presented and evaluated. Finally, we analyze briefly problems related to anycasting in dynamic routing and multi-layer networks.