Splitting a P2P video distribution in multiple media flows with different priorities is an interesting approach for developing flexible and adaptive streaming systems, ranging from VoD to TV. Such an approach can both yield satisfactory quality to all end users and be light in network resources usage, because low-priority flows can be discarded a-priori when target peers do not have enough resources to receive them. This paper focuses on chunk-based video distribution in unstructured meshes, adopting a push strategy (the sender takes the scheduling decision) based on buffer map exchange to avoid sending duplicated chunks. A deadline-based scheduling algorithm is proposed, where different flows of chunks are prioritized using different deadline postponing parameters for each flow. Some experimental results show good differentiation properties and streaming performance much better than with strict priority enforcement. Also, PSNR measures on real video streams show improvements compared ...