From the outset, Community law had an absolute authority on national law. The primacy of the EU law has always been one of its fundamental characteristics which ensures its uniform application on the territory of the Member States. The respect of the national identity, introduced to the primary law since the treaty of Maastricht, aims to give a margin of discretion to MS and to counterbalance the effects of the integration. The process of exceptional integration offered by the EU is marked by successes and failures. The EU has to deal with very difficult European issues, with crises at different levels, concerning the euro zone, the immigration, the lack of confidence of European citizens at the European institutions highlighted by the BREXIT. Does the EU have the capacity to respond at the crises? The challenge to be taken up is to achieve the modernity of the EU law by renewing the concept of integration. The respect of national identity by the EU which paves the way to a supranational identity could be the appropriate remedy to the conflicting relations between national law et EU law.