The present invention relates to a method for streaming, on a player of a client device (11), a broadcast content within a peer-to-peer network (10) of client devices (11, 12), said content consisting of a sequence of segments available in a plurality of levels of quality and said player being adapted to choose the level of quality of the segments in accordance with an adaptive bitrate ABR regulation logic; the client device (11) comprising a first buffer (M1) adapted to store segments in a format suitable for transfer within the peer-to-peer network (10), the method being characterized in that it comprises the implementation, by data processing means (110) of the device (11), of steps of: a. Receiving a request for a segment from the player; b. Providing, in response, said segment from the first buffer (M1) upon expiry of a response deadline defined with respect to said ABR logic of the player.