The article presents the experience of organizing preventive work with the problem of destructive aggression of university students. Young people as a certain socio-psychological group, with their age characteristics, are the most vulnerable to the effects of destructive discourse. The article analyzes the problem of the manifestation of destructive behavior, considers the causes, types, forms of its manifestation in the youth environment. A special place is occupied by the negative impact of cyberbullying on the mental health of its victims. Presented are methods for diagnosing a tendency to destructive aggression used by the Center for Socio-Psychological Support of Students of NSUU to identify students at risk, some diagnostic results are given. The most common cases of cyberbullying in the practice of a university psychologist are described.Some characterological features and personal properties of students - aggressors were revealed. The experience of the Center for Social and Psychological Support of Students on monitoring, analysis, interpretation of markers of destructive aggression in social networks is presented. A model of a comprehensive program of preventive measures in the conditions of educational institutions for the recognition and prevention of destructive aggression has been developed, which includes primary, secondary, tertiary prevention.