The discipline of organizational behaviour along with organizational theory  and general management is essential in training of managers including those of public sector. However, it is a relatively new academic discipline for Russian higher education institutions. The article says that the main specific feature of this discipline is that it is founded on the complex of ideas and concepts belonging to various basic fields of knowledge. This, in its turn, poses a number of challenges in working up and delivering the course. Understanding of these problems is imperative, much of it is owed to the peculiarities of OB establishing as a separate research area in the 50-60ies of the last century. Therefore, the article rather comprehensively describes the establishment history of organizational studies in science and analyses the basic factors having the most significant influence on the process. Thus, the article gives a thorough consideration to a valuable contribution made by F. Taylor, who put forward a concept of scientific management; M. Weber, known as a founder of the bureaucratic form of organization, clearly differentiating between managers and executors; A. Fayol, who maintained his attitude towards the division of labour – practices assigning people with special tasks to their best ability; E. Mayo, who proposed the idea that social environment at work significantly affected productivity; K. Levin, who considered it was person’s personality as well as his/her environment that determined human behaviour. These scholars, first, contributed to grasping the idea that behaviour at work was shaped by a set of individual, group and organizational factors, second, with organizational behaviour studies generalized, to establishing a unified science. Extensive researches carried out, with the conclusions published in the article known as the “Gordon and Howell” report in 1959, were the key factors in establishing of OB as a science. Thus, it’s underlined that the present-day OB is a science generated from various social disciplines (psychology, social psychology, political science and anthropology). Thus, interdisciplinary character of OB presents one of the main challenges – while working out the organizational behaviour course, a teacher should adjust his/her approach and develop his/her area of competence in comparison to his/her basic education, and should ensure balance in core constituent elements representation, when describing phenomena and concepts of organizational behaviour. Otherwise, the course might turn into a summary of the “Psychology of Management” or the “Sociology of Management”, and might not fulfill its integrative function. Hereafter the article scrutinizes a list of topics studied by OB and concludes that there is a wide range of OB issues, even simple enumeration of the crucial issues proves it: individual behaviour management, group management, organizational process management, motivation of employees, organizational culture establishing. Thus, another challenge is being set forth – comprehensive presentation of all the aspects of this discipline in a study course poses a rather challenging task. Third challenge, from the author’s perspective, manifests itself in a fact that contemporary organizational theory studies both various types of organizational behaviour and manifold versions of organizational behaviour as well as means of interpreting them. For the most part it is determined by diversity of approaches to organizational theory in psychology, sociology and other behavioral sciences. Thus, psychological science distinguishes between at least six markedly different methodological aspects. The article pays most  ttention to the methodology of individual differences, behavioural, non-behavioural and psychoanalytical approaches. Sociological and social  nthropological approaches, which are the basics for interpretation of organizational behaviour variation, encompass much more – nine, at least. Taking  into account the abovementioned, the author formulates the forth challenge – how to share extensive knowledge acquired in the area of OB as  a managerial science, within managerial education study course in higher education institution and avoid conceptual narrowness resulting from teacher’s commitment to one or another approach. Lastly, we approached the fifth challenge. It is determined by the fact that OB rests upon the researches enriching the discipline of organizational behaviour. Unfortunately, in present-day Russia this discipline represents a “calque” from the American model. Both theoretical and practical researches in various aspects of organizational behaviour in Russian institutions are indispensable to overcome this drawback. Moreover, it is crucial to disclose national specifics of human behaviour at work and opportunity to apply it in order to  increase productivity. In support of the abovementioned, the author produces the results of the research conducted in the early nineties in Russia. This research is grounded on the approach to analysis of differences between nations, suggested by G. Hofstede, and goal of the research was – to determine how the Russian national culture affects human behaviour in an institution.