The article is devoted to issues of globalization in the sphere of judicial proceedings. The author proves that it has nature, which comes from general globalization process. Separate issues of globalization demonstration were considered, including, the establishment of so-called extra-national legal procedural system as a consequence of rising internationalization of procedural mechanisms and its further interaction with national systems of judicial proceedings under descending internationalization. It is based on the idea of fundamentalization of human rights and securing the accessibility of justice as an international standard of just judicial proceedings. Its main peculiarity consists of the unification of judicial procedures of civil cases consideration in order to secure their effectiveness, as well as harmonization of procedural legislation within the EU.