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A group of hosts which belong to a particular IP address and inter-networked need to be coordinated, organized and managed for their network activities. Multicast and anycast are the popular group services used for group network activities. This group of hosts in one or more networks requires a management service that allows new members to join or leave as they wish. This information is then used by end host to acquire group services. In IPA and IPv6 multicast, Internet Group Management Protocol (IGMP) and Multicast Listener Discovery (MLD) are being used for group membership management. However the new communication paradigm anycast, is lack of such mechanism for its Group Membership Management (GMM). This paper proposes a new protocol known as Anycast Group Membership Management Protocol (AGMP) to support global anycast GMM. Existing multicast GMM has been explored and distinguished with our proposed AGW. AGW solution is not expensive in terms of memory and computation. It is scalable to support large numbers of groups and members per group. Design and simulated implementation results of the group membership behavior is presented in this paper.