Method of connection set-up between several networks of a mobile radio system

The connection system allows a connection to be established between a first mobile radio network (PLMN1) and a mobile station within a second mobile radio network (PLMN3). The originating switching control (OMSC) of the first network addresses data stored in a home location register (HLR) of the mobile station network, to allow a direct connection for speech and/or data to be established, without insertion of the home public land mobile network (HPLMN) in the connection path, using the accessed data, a country code and a network code.