A method an system for establishing a multi-user communication session, having a session description, between terminals with incompatible media characteristics, in which users with terminals having incompatible media characteristics are invited to participate in the communication session. A transcoding session is set up for enabling transcoding between the incompatible media characteristics of the terminals based on information about the terminals of the users having accepted the invitation, this information comprising the media characteristics of the users' terminals. The session description is established according to the transcoding session and, during the communication session, media streams from the terminal of one user are transcoded according to the transcoding session and the transcoded media streams are transmitted according to the session description to the other users participating in the communication session, using the media characteristics of the terminals of those other users.