In the last decades in the European Union the cross-borders interchanges have been increased so much. The administration of justice had to adapt itself to the new circumstances too, especially against the cross-borders crimes. Fort that reason, one of the aims to reacg was improving of the criminal procedures effectiveness, by fostering the cooperation betwenn judicial authorities situated in different jurisdictions. For the gradual creation of a European Judicial Space, the Members States had to adopt some measures to simplify an accelerate the judicial assistance and the main instrument has been the Convention of May of 2000 that, in addition to general rules that improve the direct and fast relationship between tribunals, introduces also numerous specific forms of cooperation which they must be examined.