We have entered the new millennium with two great inventions, the Internet and mobile telecommunication, and a remarkable trend of network evolution toward convergence of these two achievements. It is an evident step to combine the advantages of the Internet and the mobile communication methods together in addition to converge the voice and data into a common packet-based and heterogeneous network infrastructure. To provide interworking, the future systems have to be based on a universal and widespread network protocol, such as Internet protocol (IP) which is capable of connecting the various wired and wireless networks (Macker, Park, & Corson, 2001).However, the current version of IP has problems in mobile wireless networks; the address range is limited, IPv4 is not suitable to efficiently manage mobility, support real-time services, security, and other enhanced features. The next version, IPv6 fixes the problems and also adds many improvements to IPv4, such as extended address space, routing, quality of service, security (IPSec), network autoconfiguration and integrated mobility support (Mobile IPv6).Today’s IP communication is mainly based on unicast (one-to-one) delivery mode. However it is not the only method in use: other delivery possibilities, such as broadcast (one-to-all), multicast (one-to-many) and anycast (one-to-one-of-many) are available. Partridge, Mendez, and Milliken (1993) proposed the host anycasting service for the first time in RFC 1546. The basic idea behind the anycast networking paradigm is to separate the service identifier from the physical host, and enable the service to act as a logical entity of the network. This idea of anycasting can be achieved in different layers (e.g., network and application layers) and they have both strengths and weaknesses as well. We focus on network-layer anycasting in this article, where a node sends a packet to an anycast address and the network will deliver the packet to at least one, and preferably only one of the competent hosts. This approach makes anycasting a kind of group communication in that a group of hosts are specified for a service represented by an anycast address and underlying routing algorithms are supposed to find out the appropriate destination for an anycast destined packet.