The development of the modern higher school is characterized by a number of trends that cannot always be called positive. The recent reforms in the sphere of higher education in Russia increase uncertainty of the conditions, in which institutions of higher education currently function. The topicality of the problem makes it necessary to study the problem of reputation management of the higher school, to consider various approaches to creation of reputational responsibility and positive reputation of a university as important tools to improve the university's operating efficiency, and to achieve competitive advantages in the higher education market. The purpose of the article is to consider approaches to the problems of reputation management of a higher education institution based on studying the processes of creating a positive reputation of a university by increasing its reputational responsibility, identifying reputational risks and other factors. In particular, the authors examine theoretical aspects of the reputation management in a university, analyze the results of studying characteristic features of creating the university's reputation and its reputational responsibility.