The interfacing of coded media data packets in the transfer from and to a peer-to-peer network envisages that the data packets are included in groups of packets that may have lengths different from one another. Each group of data packets is encapsulated in a group of chunks of given length. The media data is made available in the network as a multiplicity of different descriptions of a multiple-description coding of one and the same media content. The terminals of the peer-to-peer network are configured for accessing selectively the multiplicity of different descriptions of said media contents, combining them with one another, or else accessing one of the different descriptions in substitution for another preserving access to the media contents. The data may be made available as base layer and at least one enhancement layer of one and the same media content.