A method for automatically configuring a router (10) that has at least one upstream interface (11), connected or connectable to a higher-level subnetwork and / or a higher-level router, and at least one downstream interface (12), connected or connectable to a lower-level subnetwork (5), wherein it is monitored whether the router (10) receives, on the at least one upstream interface (11), messages providing notification of at least one domain, in particular as part of a DNS search list option (21), and, if no such message has been received over a prescribed period, a DNS island mode is automatically activated in which the DNS zone (22) of a local DNS server (14) of the router (10) is configured using a predefined island domain, and a transmission module (13) of the router (10) is prompted to send at least one message via at least one downstream interface (12), which message comprises the preconfigured island domain, in particular as part of a DNS search list option (31), and preferably an address (23) of the downstream interface (12). The invention furthermore relates to a method for automatic address configuration, a router (10), a computer program and a computer-readable medium.