Based on previous work on the phenomenon of the dissemination of the oral heritage of the French in America, viewed from the perspective of the transfer of European traditions of storytelling, song, oaths and rituals among minority groups, this communication wants to propose the elements of an interpretative model that could illustrate the amplitude and account for the dynamics involved. The “principle of the snail” could cast an original and significant light on these questions by exposing the relations between center and periphery, the possible crossings or the plural origin of the traditions; it would help to identify the factors that maintain or erode traditions by explaining why margins are better and longer-lasting for transmitted messages that are eroding at the center.