The work focuses on the interplay between European Community Law and constitutional law of the Member States of the EU. The non-existence of a written supremacy clause in European Law leaves a wide margin for interpretation. The European Court of Justice (ECJ) characterizes European Community Law as supreme, directly effective and autonomous. Behind these structural elements lurks the fundamental dogmatic question of the dependence of European Law on national law. As European Law is founded on international treaties, Member States` Supreme Courts tend to argue that treaty law can not be completely autonomous in their internal legal order. In their opinion and in opposition to the ECJ, the rule deciding whether national or European Law should be supreme is located within the national constitutional order. The work is divided into four chapters. Chapter 1 gives an introduction to the ECJ`s view on the supremacy of European Community Law. Chapter 2 focuses on the effects of supremacy, direct effects and the obligation to interpret national law in conformity with Community Law on Member States` rules regarding the competences of national authorities. Chapter 3 describes the case-law of the ECJ regarding the supremacy of Community Law in proportion to national constitutional law and overviews the respective case-law of the Member States` Supreme Courts. Chapter 4 describes the Austrian model of opening the legal order for European Community Law and scrutinizes the case-law of the Austrian Constitutional Court concerning the interplay between European Community Law and Austrian constitutional law.