Globalization has changed the face of the world, gave rise to the restructuring of society, the transformation of the state and its sovereignty and led to the "denationalization" of law. Today, the future of law is formed, which must be adequate to the new society. The greatest changes occur in international private law, where we are witnessing an increase in the number of norm-making actors with norm-making being adhocratic in nature; strengthening and modification of the delocalization process of law, standardization and the search for new legal identity; an unprecedented growth of the bulk of non-state regulation norms and searching for ways to legitimize them; the active development of alternative non-state and supranational systems for transboundary dispute resolution; paradigmatic shifts in the field of law, due to the interpretation of the concept of "rules of law"; updating of the institute of autonomous legal qualification, etc. The privatization of law contributes to its fragmentation, which in the framework of private international has two areas of development: normative and institutional. All this creates an effect of "parallel" social realities, with two, in fact, colliding systems of regulating transboundary relationships and two dispute resolution systems based on state law and non-state law, developing. The emerging new society and a new civilization form the request for a new law, which is in search of its new identity. Incurred in connection with this doctrines of global /transnational /non-state law require their understanding and conceptualization, and a new social practice: lexinformatica, lex digitalis, lex electronica or lex networkia, sportiv. lex, lex constructionis, lex laborisinternationalis, - need to be adopted to the modern paradigm of private international law. The article explores the multi-layered normative pluralist architecture, and makes some assumptions about the future regulatory landscape with regard to cross-border private-law relations. The emerging world order, the center of which is the global economy with supporting cross-border private-law relations, still governed by the law emanating from the state, but the latter loses its regulatory monopoly, and therefore require a rethinking of the normative superstructure and the formation of a new legal language, able to explain and comprehend the effects of globalization in the legal field.