Author deals in this contribution with the question of international legal arrangement of the institute of prescription like a title of acquisition of the state territory. He tries to fix the existing form of the mentioned legal arrangement by analysing the roman legal arrangement of the Roman law usucapio institute and its influence to this arrangement, by analysing the relevant opinions of legal scholars and experts and by analysing the relevant international jurisprudence. In conclusions author states that the international legal institute of prescription was created under the pattern of the Roman law usucapio institute under the principle of analogy of law. The relevant opinions of the international law science presume that the prescription of the state territory could by applied successfully if the possession of the territory is undisturbed, uninterrupted, carried out in a sovereign capacity, publicly, peacefully, without protest or competing activity by the existing sovereign, and for sufficiently long time. Author also states that there are some opinions which deny that the institution of prescription plays any role in international law. However, analysis of existing international jurisprudence allows author to come to the conclusion that the concept of prescription of the state territory more likely does exist in the form of international custom. Author describes several cases when the notion of prescription was used in the jurisprudence what shows that there is relevant international customary practice confirming the existence of the international legal arrangement of prescription like a title of acquisition of the territory.