The article reveals the uncertainties and antagonisms of the legislative regulation of administrative control and supervision proceedings, which have emerged as part of the modern non-judicial administrative enforcement process in the Russian Federation. In order to overcome the identified problems, a scientifically substantiated extrapolation of the well-known institution of obligation is carried out for administrative and procedural legal relations arising from the implementation of a control (supervisory) body's legally binding order to eliminate the identified violations of mandatory requirements. It is concluded that the presented scientific approaches can be effectively and efficiently used to develop comprehensive changes and additions to the Federal Law “On State Control (Supervision) and Municipal Control in the Russian Federation”, federal laws on types of control, as well as the Code of Administrative Offenses of the Russian Federation, in order to optimize the voluntary and compulsory execution of a legally enforceable order issued by a control (supervisory) body to eliminate identified violations of mandatory requirements.