European legal integration studies are witnessing a major renewal of the empirical data. Today, the theoreticalmatter of the hierarchy between EU law and national constitutions is turning to a real risk of constitutional conflictwhich is seen by European supreme judges (ECJ and constitutional courts) as a real threat on the Europeanconstruction in itself. But how to manage this since there is no proper legal solution according to the legalparadigm of norms' hierarchy? The current situation for European supreme judges is a theoretical stalemate and areal practical dilemma, under the shadow a 'nuclear threat'.Because the ECJ and the national supreme courts are in a situation of anarchy, they cannot answer to thequestion of legal hierarchy; they could only circumvent it or prevent themselves to be in a situation where theyhave to face that question. I argue that the relationship between European supreme judges is shifting from abilateral mode (like classic international relations) to a governance mode: the 'constitutional governance ofEuropean supreme courts'. Behind, there is a shift from a Lockean culture to a Kantian culture of anarchy. Thegovernance mode pertains to establish a horizontal, transnational and deliberative network of formally sovereignactors, in a security community-like system, which permits to tune up their constitutional judicial decisions anddefine a common way to handle the dilemma of the national and EU legal orders' articulation. They tend to forman epistemic community by adopting the same way of seeing the problem and eventually the same legal values,according to a logic of appropriateness.
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