The present invention relates to a method for continuously reading, on a client device (11), content broadcast within a peer-to-peer network (10) of client devices (11, 12), said content being made up of a sequence of segments, the client device (11) comprising a first buffer memory (M1) provisionally storing at least one raw segment of said content, each raw segment being in a format that is suitable for transfer within the peer-to-peer network (10), the method being characterized in that it includes the implementation by data-processing means (110) of the device (11) of the following steps: (a) converting at least one raw segment from the first buffer memory (M1) into a format suitable for reading on the device (11), and storing said converted segment in a second buffer memory (M2) of the device (11), so that the second buffer memory (M2) stores a number between a minimum number and a maximum number of converted segments arranged upstream from a reading point of said content; (b) reading, from the second buffer memory (M2), at least one fragment of the converted segment arranged at said reading point; (c) deleting, from said second buffer memory (M2), at least one converted segment arranged downstream from said reading point, so that the second buffer memory (M2) stores a number no higher than a maximum number of converted segments arranged downstream from a reading point of said content, the associated raw segment being stored provisionally in the first buffer memory (M1).