1. A method of exchanging messages between a first mobile terminal which is part of a first message domain and at least one second mobile terminal which is part of a second message domain, each domain including at least one mobile radio network, one message server conforming to a first standard, referred to as the enhanced message service/short message service standard, and/or one message server conforming to a second standard, referred to as the multimedia message service standard, which method includes the following steps: initiation of a message conforming to said first standard from a first terminal to at least one second terminal not compatible with said first standard to which said initiated message conforms; transmission of said message by said message server conforming to said first standard to a message gateway including a database comprising a table of message profiles of terminals belonging to a message domain with which said gateway is associated; conversion by said message gateway of said initiated message conforming to said first standard into a message conforming to said second standard supported by said destination terminal or terminals; transmission of the converted message conforming to said second standard by said message gateway to said message server conforming to said second standard; and delivery of said message conforming to said second standard by said server conforming to said second standard to said destination terminal or terminals.