Today challenging task in IPv6 to configure themselves independently and extend address space between IPv4 to IPv6 using different techniques. Several terms and techniques are necessary to understand Dual-Stack Mobile IP to auto-configuration in IP Networking. The IP mechanism for auto-configuration of addresses depends on the Dynamic Host Configuration Protocol (DHCP) server determination of whether addresses should be obtained using the configuration mechanism procedure. Mobile IP is technology allows mobile device users to move from one network to another IP address. And Dual –Stack mechanism supported both IPv4 and IPv6 traffic and routes with independently work hosts and routers, and to control the mobility between mobile and DHCPv6 server, signal traffic of hosts and routers, so this paper main aim to a comparative study on the auto-configuration in Dual Stack and Mobile IPv6 using co-existence techniques.