Abstract: The regulation of the application of an arbitration clause as a type of arbitration agreement is based on the dual nature of this legal category, which determines the specifics of the relationship between material and procedural legal relations when the latter arises within the parameters established by the arbitration clause. In such cases, a significant simplification of legal regulation is not excluded, when it is possible to recognize signs of accessory in such relationships.
According to the results of the study, the author proves that the interrelationships of material and procedural legal relations arising from the application of the arbitration clause have accessory characteristics according to eight criteria usually highlighted in the literature. It is proposed not only to establish such an approach to defining the features of accessory in this particular case in the doctrine, but also to improve the current legislation and practice of its application. In the work, the practical consequences of the author's conclusions are shown by the example of simplifying the procedure for verifying the possibility of applying for enforcement of decisions on interim measures taken by a court of another jurisdiction (international arbitration court) under an agreement containing an appropriate arbitration clause, "recognized" by national jurisdiction, where enforcement of a decision on interim measures is assumed. The work is based on the application of a whole range of general and private scientific research methods and techniques, the main of which were the method of system analysis and the method of formal logic in the form of deduction and induction. Accessory relationships remain a little-studied legal phenomenon, both in the theory of law and in branches of legal science. The most in-depth and consistent studies of this issue are present in substantive law, where they relate mainly to the problems of establishing the presence or absence of an accessory relationship between contractual obligations and ways to ensure the fulfillment of obligations. In procedural law, accessory as an independent legal category is not studied, although certain institutions of procedural law, for example, interim measures in civil proceedings, clearly have separate signs of accessory in their regulation. It seems that the establishment of the properties of accessory in the relationship between substantive and procedural legal relations, when the parameters of the latter are determined by an arbitration clause, will have important theoretical and practical significance.