1. A method for establishing a connection from a network-internal terminal of a packet-based communication network to a network-external connection destination, the method comprising the steps of: transmitting, via the terminal logical address information that identifies the network-external connection destination to a central connection controller provided for controlling and managing network-internal connections; determining, via the connection controller, a gateway device of the communication network as the connection destination based on the transmitted logical address information; establishing a connection controlled by the connection controller between the terminal and the gateway device; transmitting, via the terminal, the logical address information to the gateway device; determining, via the gateway device, a network-externally valid transport address which is assigned to the transmitted logical address information; addressing, via the gateway device, the network-external connection destination in a relaying, packet-based communication network; and relaying the connection over the relaying communication network to the external connection destination based on the network-externally valid transport address.