Abstract: The network comprises a tree specialized in sending information signals upstream, comprising optical-fibre branches. In a junction (L5), an opto-electric conversion is performed in a receiver (RPR5, RPR6) and an electro-optical conversion in a transmitter (RPE2). In the electrical part of a junction, the transmitter of the junction (RPE2) polls the receivers of the junction (RPR5, RPR6) to receive therefrom the messages coming from downstream (5 . . . 6 . . . 5 . . . 6 . . . ), after which a message of local origin (S) is added to those coming from downstream. Although, as a result of the polling, there is no synchronism between the retransmission and the reception of the given message, a specific process makes it possible to ensure that the messages reach an upstream receiver (RPR2) in a predetermined order (S X 5 X 6 X S X 5 X 6 . . . ), which makes it possible to recognize when all the messages have been received well.