While the European Union is in the process of carefully navigating among the various forms of sub-federalism, Member States - including recent ones like Hungary, trying to find an equilibrium between their sovereignty and European supranationalism - have to cope with possible conflicts between their national legal systems and EU law. Since Hungary's accession to the European Union, the Hungarian Constitutional Court has faced questions regarding the constitutionality of EU legal rules and conflicts between European and national legal norms. This article examines these issues and analyzes criteria of constitutional review that the Court has gradually set out in dealing with some of these conflicts. So far, it has established two principles marking the boundaries of future constitutional practice. First, it will treat the founding and amending treaties of the European Union as part of domestic law for the purposes of constitutional review, thereby setting up a two-tier system of legal rules applicable within Hungarian legal practice instead of a possible three-tier construction that would distinguish between national, international and European law. Second, in the absence of jurisdiction to review substantive (un)constitutionality (as opposed to procedural constitutionality), the Constitutional Court does not regard a conflict between domestic law and EU law as a constitutionality issue and this mandates the ordinary courts to resolve such conflict of a sub-constitutional nature. Taking these conclusions as starting points, this article sets out the possible types of conflicts that may occur between EU rules and other legal rules applicable in Hungary, weighing the constitutional relevance of these conflicts; it also outlines the directions along which the practice of the Hungarian Constitutional Court may develop in this respect.