In a digital telecommunications network having first and second addressing zones, a name and address server in the first addressing zone receiving from a first address of the first zone, assigned to a source machine, a request to provide an address in relation to the name of a destination machine situated in the second addressing zone, sends to a second address of the first zone a first packet containing at least the said name of destination machine, said second address of the first zone being associated in a static manner to a first address of the second zone, assigned to a management unit. The management unit sends to an interface a second packet destined for the name and address server comprising as origin address, a second address of the second zone assigned to the destination machine. The interface transmits the second packet to the name and address server while replacing the origin address by a third address of the first zone, forming part of a list of addresses of the first zone, forming part of a list of addresses of the first zone allotted to the second addressing zone and associated in a dynamic manner with the second address of the second zone. The name and address server includes this third address in a response to the address provision request returned to the first address of the first zone.