Abstract. In the article, different reasons for the long-lasting war against international terrorism under the Islamist banner are analysed. Notwithstanding the "Al-Qaeda's" weakening, since autumn 2001, many new groups have sprung up threatening the international security. Till now, the war has been waged only against terrorists, but no serious attention has been paid to neutralization of radical Islamism as an ideology causing terrorism. In connection with the military actions in Iraq and Afghanistan, anti-western feelings have been growing up breeding radical Islamism. It is emphasized in the article that the antiterrorist coalition in its present state is unable to fulfill its mission. It can become really efficient only if Muslim régimes would increase their input into the common struggle. Standing on the ground of traditional Islam they could easier curb Islamism and thus cut the roots of terrorism.