In the beginning of the article the author stresses that by the end of the previous century in the framework of the European Union there existed several documents governing the issue of criminal extradition. The author describes the history of elaboration of the principle of mutual acceptance of documents in the sphere of law-enforcement and particularly in the question of extradition in the form of “framework resolution” of the European Union. Apart from the history of the resolution the author also gives an in-depth analysis of its contents, including the procedure of its implementation.Further on the reports of the European Commission on the implementation of the European arrest warrant are analyzed. In these reports the results of the work in this sphere are commended and characterized as positive. But the author points out the notice of the European Commission that this should not lead to weakening of the efforts of states not fully complying with the requirements. Then the author enumerates the difficulties existing in this respect.In the conclusion the author states that the practice of implementation of warrant requires an enhancement to the procedure and that there should be worked out some guidelines for the effective implementation of the warrant.