“Extremism” and “terrorism” qua pure concepts reflect in its abstract meaning any excessiveness in actions and counteractions of cooperating subjects, which gives grounds to define aforementioned concepts diversely within different paradigms of the analysis of phenomena, in which excessiveness prevails. Within the scope of conflictological paradigm of analysis, extremism and terrorism is nothing more than such a mean of cooperation, where actions of the opposite side exceed reigning rules of cooperation in a society and actualize the scramble via instruments of destruction by lowering the attained level of social classes’ peaceful coexistence in a society. Ultimately, conflictological analytics proceeds from the understanding of extremism and terrorism as specific forms of negative cooperation as a result of which through destruction of attained peace the effort to halt material progress and to provide a background for preserving existing relations, which affected by modern technological premises require global changes in property relations, is being carried out. Two trends standing in opposition to each other, which most strikingly are represented in the European Union, one of which is related to the emancipation of the people from poverty, meanwhile the other is related to the conservation of this poverty on a widening scale, bring into being the extremism as a reaction of Europe’s ruling classes to a strengthening movement of employees for social equality in possession and consumption. The global change of all the cooperation means toward the struggle as a counter to social peace is the symptom of imminent social disaster, entailing tectonic shift in the property relations. The scientific refusal of the understanding of extremism’s social determinism gives birth to the ideological barbarity in real life, which returns individuals, whole political parties and folks to ideological paradigms of the Middle Ages.