The main goal of this article was to present the proceeding concerning the european warrant of arrest, in context of selected issues which exposes his cross-border capacity. The article addresses to jurisdiction, in order to show that, informalizing of extradition, in practice presupposes making necessary of interpretation rule of law, in scope which allows to determine the goal and frame of international cooperation in penal cases. The analysis of framework of union decision, allows state that assumption of procedure’s creators, how to speed and improve the procedure, nowadays requires of revision concerning the key issues. General clauses of procedure, casuistry indicating to new legal premises which govern the extradite, also due to presumption of shortage of standards in scope guarantees ensuring reliable lawsuit, result in prolongation of procedure. Outlaw aspects of procedure on level of international cooperation, institutional, organizational, also regarding political system of counties, allows to state, that role of limited recognize and rule of limited trust is functioning.