The stuhy is anchored in reality, that reagarding of the criminal phenon in the organiyed crime of dealing, of the traffic of weapons and perons, serious crimes exceed the boudari es of certain states and examines the measure which to be taken to fimly repress such crimes. The study introduce a serises of preoccupations in order to harmonize the law depositions of material and procedural criminal law, a gradual increase of the mutua l confidence in the judicial acts of the member state of the European Union and the enlargement of the cooperation between the judicial bodies in view of preventing serious criminel deeds. We espress our conviction that sooner or later there will be an Eur opean Criminal Cod an European criminal procedure with unifying dispotions, in parallel with the national criminal legislation.