The EU is a structure which is positioned “in-between” hierarchically organized nation-state governing structures and heterarchically structured global governance structures. Thus, the EU is a hybrid which partly relies on governing and partly on governance. This two-dimensionality is the central reason why the question of the constitutional character of the EU remains fundamentally unresolved. Thus, it is proposed that the EU should aim for the development of a constitutional form aimed at alleviating the tensions inherent in the European construction through a conflict of laws approach. In order to respect the hybridity of the Union, such an approach will however have to be based on a three-dimensional conflict of laws concept insofar as it would have to take account of horizontal conflicts between territorial units, vertical conflicts between the EU and its ember states as well as horizontal conflicts between the functionally differentiated structures of the wider society.