Method of switching over an audiovisual session in a telecommunications network comprising at least one first access network and one second access network, an audiovisual session being in progress, during which at least one user terminal attached to said first access network and able to attach itself to said second access network receives from a contents server at least one constituent data stream of an audiovisual content by way of a data stream gateway comprising a first interface (41 S1) to said first access network and a second output interface (41 S2) to said second access network, the audiovisual content being encoded in the form of a plurality of scaled data streams comprising a basic stream and at least one enhancement stream, said method being characterized in that, when said terminal has attached itself to said second access network, said method comprises the following steps of: - receiving a request for session switchover to the second access network, said switchover request having been emitted following a change of a state of attachment of said terminal to said second network; - ordering switchover of said audiovisual session at said data stream gateway from the first output interface to the second output interface; - recovering information related to a context of said audiovisual session switched over to the second interface; - ordering evaluation at a contents profiles server of an adaptation of quality, that can be supported by said second interface, of the audiovisual content transmitted for said audiovisual session as a function of said information recovered; - receiving a response on the part of said contents profiles server and requesting updating of said data stream emitted during said audiovisual session to the contents server so as to ensure said evaluated adaptation of quality said response of said contents profile server indicating a number of enhancement streams to be activated, - saving context information relating to the connections established between said user terminal and said data stream gateway in respect of said audiovisual session for a predetermined duration. - receiving a request for session switchover to the second access network, said switchover request having been emitted following a change of a state of attachment of said terminal to said second network; - ordering switchover of said audiovisual session at said data stream gateway from the first output interface to the second output interface; - recovering information related to a context of said audiovisual session switched over to the second interface; - ordering evaluation at a contents profiles server of an adaptation of quality, that can be supported by said second interface, of the audiovisual content transmitted for said audiovisual session as a function of said information recovered; - receiving a response on the part of said contents profiles server and requesting updating of said data stream emitted during said audiovisual session to the contents server so as to ensure said evaluated adaptation of quality said response of said contents profile server indicating a number of enhancement streams to be activated, - saving context information relating to the connections established between said user terminal and said data stream gateway in respect of said audiovisual session for a predetermined duration.