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This paper addresses the IPv6 address ownership problem. Currently, an IPv6 host communicating with another node cannot prove ownership of the claimed IP address, and that it is authorized to use such address. Although this issue has been present for long time, it has only become well known and little effort has been applied to this field. In particular, the problem of IPv6 address ownership has been identified during the development of the latest version of the mobile IPv6 protocol. Even though the IETF Mobile IP working group pointed out the problem and the threats are obvious in the mobile IP environment, the IPv6 address ownership problem is not restricted to mobile networks but affects IPv6 communications in general and is an important security problem that needs to be properly addressed. This paper describes the IPv6 address ownership problem and analyzes the current existing solutions. An alternative solution for the IPv6 address ownership problem is presented in this paper and compared to existing solutions.