The purpose of the study is to determine modern approaches to the strategy of applying the compliance system at metallurgical enterprises. From the standpoint of the theory of hypercomplex dynamic systems, the components of the metallurgical enterprise are considered. Hypercomplexity is provided by the variety of sub-sectors included in the research object. The system properties of metallurgical production are highlighted, in particular, hypercomplexity (S1), dynamism (S2) and structurality (S3). It is shown that one of the latest global scientific developments regarding the procedure for compliance with obligations in the financial and industrial spheres is the theoretical concept of Compliance. It is advisable to provide advisory functions to the Compliance system at the enterprise, when the final decision on the implementation of its recommendations is taken by the management of the enterprise at the appropriate level. It is shown that common to all theories of Compliance is finding a balance between such categories as "compliance" with established requirements and "risks" from inappropriate fulfillment of obligations. The ratio of financial risks and the probability of compliance with these risks of business entities is given. It is shown that Compliance should acquire the status of not only a controlling body, but also take into account the elements of psychology in the implementation of its activities.
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