The author deals with an important question of the Hungarian constitutional law, which plays a relevant role during the accession process of a state of the European Union (EU). It means that the question of legal haromization always arises, when a state is going to join the EU. The author focuses on the question, whether the international law-namely the law of the EU-or the national law should be privileged in given cases. The author introduces the possible conflicts between international law and domestic law with the help of several examples. He refers to the numerous solutions of member-states of the EU and also mentions the situation of some would-be member-states, too. The author highlights the point of view that the Community law precedes the constitutions of the member-states. As a result of this the Hungarian constitution has to be modified in order to meet the requirements of the legal harmonization process, which will emerge with the access of Hungary to the EU.