In this article, Immanuel Wallerstein tries to anticipate the evolution of world conflicts and structures over the next decades. In his analysis, he identifies three main cleavages which structure future global conflicts: the triadic cleavage between the United States, Europe and Japan, who compete economically; the North-South cleavage between core zones and the periphery of the world economy; and, finally, the cleavage between what he calls the "Spirit of Davos" and the "Spirit of Porto Alegre" as a conflict between alternative images of the future world order. The structure and the dynamics of each cleavage are analysed and their evolution over the next decades is anticipated.