Abstract: Extremism is a big problem in the public life of citizens. The Decree of the President of the Russian Federation laid down the main directions of countering extremism. However, in the modern world, in which computing technologies and computer equipment are constantly developing and improving, a wide range of opportunities for communication between each other opens up for citizens who are prone to illegal behavior, including for calling for certain kinds of illegal actions.
Thus, examining the administrative and legal mechanism of countering extremism, it should be noted that the subjects of counteraction are various state authorities, the key place among which is occupied by internal affairs bodies. Federal Law No. 3-FZ of February 7, 2011 "On the Police" imposed on the police a duty that is expressed in the prevention, detection and suppression of extremist activities of public associations, religious and other organizations, as well as citizens.
Preventive work on countering extremism should be carried out at the level of formation of both individual and collective consciousness among various categories of the population, a negative attitude to acts of terror. Work in this direction should be an activity aimed at forming a belief in the unacceptability of these actions in society, non-recognition of such behavior in society, tolerant and humane attitude towards others.

Abstract: The object of the study is social relations arising on the basis of legal norms regulating administrative responsibility in the commission of several administrative offenses. The subject of the study is: scientific literature, regulatory legal acts and law enforcement practice considering the commission by the same person for the second or more time after bringing to administrative responsibility an intentional administrative offense. The methodological basis of this article is formed by general and particular scientific methods of cognition, including: - dialectical method (when studying the institute of administrative responsibility, establishing links and contradictions of phenomena, implementing their legal assessment); - historical method (in the study of the evolution of the recurrence of administrative offenses, its chronological features and relationships);- interpretation of the norms of law (when studying the norms governing the issues of bringing to administrative responsibility); - system-structural (when studying the conditions and procedure for bringing to responsibility for administrative offenses); - formal legal (when analyzing the norms of administrative law, developing author's conclusions, provisions); - logical (when presenting the research topic and formulating theoretical and practical conclusions), as well as other methods. The scientific novelty of the research is determined by the justified and planned changes in administrative legislation, which determines the relevance of improving the Code of Administrative Offenses of the Russian Federation in terms of regulating issues of administrative responsibility for offenses committed by a person previously subjected to administrative punishment. Based on the analysis of modern administrative delicacy, the author concludes that it is necessary to distinguish a new form of recidivism in the multiplicity of administrative offenses. The social danger of relapse is caused by the greater danger of the act, and at the same time the identity of the perpetrator, the persistence of his antisocial views. The fact that a new intentional offense was committed by a person to whom administrative punishment measures were applied indicates that the previous punishment was insufficiently effective, which should be the basis for imposing a more severe punishment, including the basis for prejudicial elements of crimes.

Abstract: The subject of this research is the earlier and currently active norms of administrative legislation regulating the concept of legal offense as well as scientific literature devoted to this topic and statistical data on administrative offenses from the Russian case law. The author analyzes the essence of the signs of administrative offenses. The importance of this topic is substantiated the fact that the concept of legal offense is one of the main categories of the administrative law of the Russian Federation. Analysis is conducted on the various approaches of scholars in administrative law towards definition of this concept. The novelty of this research is defined by the importance of clear definition of the concept of administrative offense due to introduction of the New Code on Administrative Offenses of the Russian Federation into public discourse. Considering the sign of public danger of an administrative offense, the author proposes formulating Article 2.1 of the Code of the Russian Federation on Administrative Offenses in the following way: “Administrative offense is a committed punishable action or inaction of a private or legal entity, posing public danger, and carries administrative liability established by this Code or a law of a subject of the Russian Federation”.