The notion of international terrorism is based on two criteria: one borrowed from actions that constitute the foundation of terrorist acts, the other drawn from particular circumstances coming from a relationship with an individual or collective organization whose objective is to seriously damage public security by intimidation or terror. Since the collapse of the Soviet Union, the international community is confronted by a radical extremist organization wahhabite Al-Qaïda. The terrorist attacks organized by this movement threaten global security today. These extremist criminal terrorist acts target civilians without distinction - women and children included - because they do not consider such acts as forbidden. The international scene has become more and more threatened today by wahhabite ideology whose Saudi origins included fifteen of the nineteen suicide-bombers responsible for the September 11, 2001 attacks on New York and Washington. Faced with the problem posed by terrorism, the international community reacted, each in their own way, by taking necessary measures that conform to their own legal system. Their objectives are to reinforce repression, facilitate the work of investigators and speed up court decisions. New penal laws or new texts have been introduced by several countries in order to confront this international phenomenon. The legal responses of national laws remain until today veritable instruments of confrontation against terrorist acts. These laws serve to deepen the understanding of terrorist motivations, their methods and their goals. By basing these laws on the international directives of the GAFI (Groupe d'Action financière) and the Committee Against Terrorism (CCT), they also serve to combat the financing of terrorist movements as well as money laundering. Keywords : anti-terrorist struggle, international law, European cooperation, extremist criminal terrorist acts