Abstract: The article is devoted to the legal characteristics and the peculiarities of administrative and jurisdictional activity of customs authorities. The author investigates the legal basis and the types of administrative - jurisdictional proceedings, the order of their registration and their role and importance in the activities of the customs bodies in the Customs Union within the Eurasian Economic Union. The article focuses on the legal and organizational problems of administrative and legal regulation of administrative proceedings. The author carries out the theoretical and legal analysis of the concepts of administrative and jurisdictional activity. The main attention is paid to the development of the methods and methodology of administrative proceedings in the customs sphere. The methodological base comprises the recent achievements of epistemology. The author applies the general philosophical and theoretical methods (dialectics, the systems approach, analysis, synthesis, analogy, deduction, observation and modeling), the traditional-legal methods (formal-logical), and special sociological methods (the statistical methods, expert assessments, etc.). The author concludes that at present in order to provide legality in the customs sphere it is necessary to improve the forms and methods of procedural activities of customs bodies. The author speaks about the necessity to develop administrative-legal regulation of administrative proceedings. The novelty of the research lies in the suggestions about the development of forms and methods of public regulation of customs activities and the provision of legal and organizational guarantees of legality in the sphere of customs administration. 

Abstract: The article is devoted to the urgent issues of the subject of proving and the use of evidence in cases of administrative offences in the sphere of customs in terms of creation and functioning of the Customs Union. The author reveals the legal framework of implementation of evidence in administrative and jurisdictional proceedings of Customs authorities, as well as the procedural order of their establishing; on this basis the author defines the ways to improve their application. The author concludes that crime prevention is largely predetermined by a clear understanding of its subject. The methodology of the research is based on the modern achievements of epistemology. The study uses the general philosophical and theoretical methods (dialectics, the system method, analysis, synthesis, analogy, deduction, observation, modeling), the traditional legal methods, the methods used in empirical sociological research The article concludes that the successful solution of the problems of the proceedings on administrative offences in the sphere of customs depends on several factors, such as the timely, complete and objective clarification of the circumstances of each case, its resolution in accordance with law, enforcement of the judgment, as well as identification of the causes and the conditions leading to administrative offences.