The European Union has given birth to a unique form of judicial cooperation in the field of criminal matters, freedom of movement creating new opportunities for the cross-border criminality. In such conditions, in order to face the new challengings, there has been established the aim of the maintainance and the development of a common space of freedom, secutiry and justice.The accomplishment of such desiderata has imposed simplified procedures of cooperation between the Member states consisting in recognition and compliance of court orders outside the state without the formalities stipulated in the classical conventions regarding the international legal assistance, which had been accomplished by adopting the Framework decision on the European arrest warrant. Yet, numerous institutional courts of the European states have faced difficulties on the concordance of certain provisions in the fundamental law and the implementation law of this present decision in what concerns the sovereignty of the states, the nationality exception, the principle of legality, the principle of dual criminality. Such objections have placed the European states in front of two contrary interests, on one side that of the European integration, of judicial cooperation in the field of criminal matters and of development of common space of freedom, security and justice, and on the other side, that of the preservation of national sovereignty and of the protection of own nationals. In such context, according sovereingty an absolute value meanswaiving interdependence, cooperation, and their lacking render the sovereginty useless. To this conclusion have came, without any reserve, the majority of the European states after the terrorist attacks in the United States of America on the 11th of September 2001, events which stood at the basis of the speediness of adopting and implementing the framework decision on the European arrest warrant.