The issue of international cooperation in criminal matters has interested legal theorists and practitioners for decades. In this area of law there are certain challenges that can only be tackled by using the joint efforts of the States, which is different from the national law of the States. For this reason, certain principles of law are specific for international cooperation, and on the basis of these principles States provide legal assistance requests to each other or else create preconditions to ensure the efficient and unimpeded criminal proceedings. It is true that the principles of mutual legal assistance and recognition, and the influence of their BALTIC JOURNAL OF LAW & POLITICS ISSN 2029-0454 VOLUME 9, NUMBER 2 2016 57 alternation are not identical to all segments of international cooperation, including the development of the evidence law in the European Union. With regard to the evidence and their admissibility in Member States of the EuropeanUnion, it should be noted that this issue is still relevant, because the biggest concern of some Member States is the admissibility of evidence, when evidence is collected in one State and the admissibility of them is assessed in the other State. It would seem like a more formalized "concern", but basically it is a quite significant impulse for searching of new legal instruments in the European Union, which would be able not only ensure the acceptability (admissibility) of evidence that was collected in the foreign State in accordance with the relevant procedural form, and in the court of the State which obtained this evidence, but also the sovereignty of the State, the authenticity of the national law, and the respect for the legal culture and traditions of this State. The authors discuss the development of the law of evidence, the separate legal segments of this law, and their strengths and weaknesses in the article. Despite the fact that the effective mechanisms of evidence movement among Member States appear in modern European Union criminal justice, the latest legal instruments lack the clarity and certainty of certain procedural legal guarantees in the context of human rights protection. way as the evidence collected according to the provisions of the national law of the State (State "B") which obtained this evidence.Based on analysis of provisions of the EU law and scientific sources 2 while investigating the issue of evidence and its admissibility in the EU in the context of international cooperation in criminal matters in this article, the purpose here is to determine what optimal mechanism(s) of legal cooperation of the EU MemberStates would be suitable while collecting and transmitting to each other the evidence, in order that this evidence would correspond the requirements, which are determined for the evidence in the national law of the State that obtained the evidence. Also, considerable attention is given to the ensuring of procedural legal guarantees, in particular the right of defence of the persons that participate in the criminal proceedings. Thi...