The European Union aspires to the primacy of its entire normative production over the entire law of the Member States. On the other hand, Member States remain inflexible about the ultimate superiority of their Constitutions over any other right. The constitutional jurisdictions of States even seem to be coalescing in order to impose their respective Constitutions as the ultimate horizon. If the conflict appears insurmountable, the current relationship working between the material constitution of the Union and the Constitutions of States seems to pave the way to a convergence.