The present invention relates to a method of broadcasting a content by streaming in a peer-to-peer network (10) of client devices (11, 12, 13) which is connected to a content server (2), said content consisting of a sequence of segments stored on data storage means of the content server (2), each client device (11, 12, 13) comprising a buffer memory storing in a temporary manner at least one segment of said content, the method being characterized in that each client device (11, 12, 13) is associated with a level defining a minimal list of segments of the content that have to be stored by the buffer memory of the device (11, 12, 13), the method comprising steps of: (a) connection of a new client device (14) to the peer-to-peer network (10); (b) assignment of a level to the new client device (14) as a function of the number of client devices (11, 12, 13) associated with each level; (c) transmission to said new client device (14) from the server (2) of at least each segment of the content which is absent from the buffer memory of the new client device (14), which belongs to said list of segments of the content corresponding to the level assigned to the new client device (14).