In this paper, we present the first snap-stabilizing message forwarding protocol that uses a number of buffers per node being independent of any global parameter, that is 4 buffers per link. The protocol works on a linear chain of nodes, that is possibly an overlay on a largescale and dynamic system, e.g., Peer-to-Peer systems, Grids. . . Provided that the topology remains a linear chain and that nodes join and leave "neatly", the protocol tolerates topology changes. We expect that this protocol will be the base to get similar results on more general topologies. Key words: Dynamicity, Message Forwarding, Peer-to-Peer, Scalability, Snap-stabilization