The Declaration on the granting of independence to colonial countries and peoples of 1960 has proclaimed the necessity of bringing to a speedy and unconditional end colonialism. It specified that all peoples have the right to self-determination. The Trusteeship Council has supervised the administration of the territories placed under the trusteeship system. The primary goals of the trusteeship system were: to further international peace and security; to promote the political, economic, social and educational advancement of the inhabitance of the trust territories, etc. The Declaration on the granting of independence to colonial countries and peoples applied also to the territories, which were not under the international trusteeship system. In 1994, following the granting of independence to the Palau Island, the list of еру trust territories was closed, but the problem has not been solved. According to UN data, there are 16 territories in the world, which are not self-governing and are a heritage of the colonial period; that has allowed the authors to assume a possibility of the announcement by the UN of a Third International decade for the eradication of colonialism.