Modern transformation processes in higher education alongside with positive effects have a negative impact on the higher education system in the Russian Federation. The purpose of the article is to find the main ways to overcome corruption in the system of Russian higher education. Russian society is developing in a legalised falsification of higher education. The relevance of the article lies in the fact that the issuance of diplomas of higher education to persons who did not master full competencies is formally legalised. The study found that these problems have a number of solutions that should be applied in the Russian education system. An effective way to control the quality of educational services and to monitor the corruption in universities is empowering the student government organisations. Also, it is important to create incentives for teachers, promoting rejection of corrupt practices.