Cognitive states are typical of students’ educational activity, which is accompanied by high activity of cognitive processes. Management of this activity is impossible without the knowledge of the structure, function, and mechanisms of actualization of cognitive states in various learning situations. The research relevance of the problem of cognitive states in the context of students’ intellectual activity is due to their unique role in the regulation of the thinking process, maintaining a  steady focus on the solution of the problem within a certain period of time. The purpose of this article is to study the structure of the cognitive states that arises in the process of solving intellectual problems (through the example of carrying out R. Amthauer’s intelligence structure test). Leading methods to the study of this problem were tests with standardized questionnaires and retrospective self–reports. According to the results of factor analysis, ten key factors underlying the structure of the typical cognitive state of interest/mental stress have been identified. A system–forming factor of this condition has been emphasized, which is an “attitude” to intellectual activity in the context of the overall semantic orientation of the subject. The obtained results can be of interest to researchers in the field of psychology of emotions as well as to specialists involved in the diagnosis of students’ intellectual abilities.