A method for automatic address configuration, router, computer program, computer-readable medium and method for automatically configuring a router that has an upstream interface, connected or connectable to a higher-level subnetwork and/or a higher-level router, and a downstream interface, connected or connectable to a lower-level subnetwork, wherein whether the router receives, on the upstream interface, messages providing notification of at least one domain as part of a DNS search list option, is monitored and, if the message is not received over a prescribed period, a DNS island mode is automatically activated in which the DNS zone of a local DNS server of the router is configured using a predefined island domain, and a transmission module of the router is prompted to send a message via the downstream interface, which message includes the preconfigured island domain as part of a DNS search list option, preferably an address of the downstream interface.