IPv6 is a new version of IP protocol, which was defined in the series of RFC documents at the end of previous century. Although developments and improvements are conducted for many years already, a new standard still did not get such distribution as IPv4. The useful innovation and one of basic advantages of IPv6 protocol is a possibility of automatic assignment of addresses to the network devices. Such mode got the name SLAAC (StateLess Address AutoConfiguration). However, there are tasks, for implementation of which greater control is needed. In this case it is necessary to use the static addressing or DHCPv6 server for IPv6 protocol (stateful autoconfiguration). The aim of this work was to visualize an IPv6 network using stateless and stateful addressing modes and to reveal the features and security issues of the specific configurations. Those security issues need to be reminded to the administrators, as the big IPv6 migration is coming for small and medium businesses.