This paper considers the system of compliance contract as a further development of the theory of the social contract, social interactions and organizational leadership. Moreover, we reveal the similarities and the differences between these two concepts. In our view, compliance control represents a truly leading technology of fighting corruption in enterprises. These issues gain special importance in Russia with its widespread problems and issues such as cronyism and corruption. In parallel, the paper presents some novel literature overview and own findings that would enable to characterize the problems of the functioning of compliance systems in firms and enterprises in modern conditions both in Russian and abroad. Foreign practice confirms the success of the development of this technology which allows us to consider it as a new social institution that would be able to be used in identifying the stages of the process. All in all, we might conclude that in Russia this practice is still far from being widespread which does not allow it to be viewed as an established social institution.