The urgency of the article is conditioned by the problem of serious information threats spreading connected with the global Internet network. The authors emphasize that young people are most affected by cyber-extremism, as this social group, although an active user, is not trained consciously and critically to perceive and process the information flow that is on the Internet. The purpose of the article is to develop mechanisms for University students' readiness formation to counteract cybercrime activities. The authors present in the paper methodological, organizational and pedagogical mechanisms of students' readiness formation to counteract cyber-extremist activity. The complex of pedagogical conditions is developed: identification of cases of cyber extremism and coordination of social and personal values of students; and the development of reflexive position of students for security in cyberspace; development of the experience of students on prevention of cyber extremism in the preparation of educational projects; the teachers' functions' description (informational, motivational and Advisory, consulting) and functions of University students' readiness to counter cyber-extremist activities (adaptation, functions of self-determination and self-realization). The scientific and methodical resource presented in the article creates conditions for increasing the level of students' readiness to counteract cyber-extremist activities.