It might sound strange that I question the possibility of the dialogue between the two civilizations at the time when there is so much talk around about the significance of that dialogue. It is true that the most respectable international organizations, like the UNO, the governments of the states, the prominent public spokesmen everywhere speak about the dialogue between civilizations. Yet, let us be frank to ourselves, little have been achieved to eliminate tension, hostility, aggressiveness. Wars and terrorist actions are increasing in numbers. It is quite legitimate then to ask the above question keeping in mind that we talk about the dialogue in the context of a new world situation-in the times of globalization. There are certainly those who will answer to the question negatively. Some of them “respond” by actions: launching wars and terrorist attacks. These are those who not only disbelieve in dialogues, but strongly resist the latter due to different reasons (mostly, of quite selfish political and economic reasons).The only way to prevent that dangerous cause of the developments is to oppose it by putting a really strong pressure on behalf of the widest public opinion. And it is here where the role and responsibility of the intellectuals are of the greatest importance. Unfortunately, even among the enlightened minds there are disbelievers in a possibility and fruitfulness of the dialogue. A few months ago, in June of this year, at the Ninths East-West Philosophers’ Conference in Honolulu one of the most respected and prominent philosophers admitted that he doubted usefulness of intercultural dialogues about which there is so much fuss. Cultural plurality, to his view, will become as useless as differences in currencies since the process of cultural hybridization would result eventually in the unification of all cultures in one. Unanimity does not exist even in the ranks of those, who formally accept the dialogue of cultures. They greatly differ in the understanding of its final purposes. To a few the dialogue should be aimed at the creation of one (their own) civilization dominant on the others by “convincing” the latter in its superiority. Some claim “the European mission civilizatrice” which eventually will make the rest of the world to “see the advantage of a democratic way of life”. The others, like Francis Fukyama, declare “the end of history because there is only one system that will continue to dominate world politics, that of the liberal-democratic West”. He is sure that time is on the side of modernity, and “see no lack of US will to prevail”. The strongest opposition to the above mentioned claims comes from the side of the Muslim world. The resistance comes from many sides: from those who are in power or fight for it, from masses who suffer of social injustice, from religious fanatics, etc. The Muslims not only resist, they often make their own claims for the dominance. In recent years one can notice drastic changes in the mood of Muslim academic community which has been driven in the above mentioned direction. Prominent professor of philosophy (Cairo University) Hassan Hanafi states: