Abstract. The article is referred to a hard way of the European Arrest Warrant adoption, which became the first tool in the field of judicial cooperation on criminal cases having embodied the judicial decisions mutual recognition principle. The foundation of a single European Arrest Warrant with due regard to all existing problems of its appliance is a significant breakthrough in the EU states cooperation, given that it forces them to rely on each other's legislation. The European Warrant was designed to efface national boundaries in the sphere of court cooperation, to establish a "freedom of movement" and a single market of judicial decisions.