An uplink group call channel is assigned to a second user who acts as the new speaker in order to switch the speaker function from a first user to the second user in an on-going group call within a mobile radio system. The mobile radio system has at least one main mobile exchange and at least one secondary mobile exchange, to each of which at least one base station system is connected. Once the uplink group call channel has been assigned, transmission of data, especially group application data, is initiated via a group call control message to at least one listening user of the group call, particularly the first user. The group call control message is generated by the second user and is transmitted to the main mobile exchange via the uplink group call channel.