The author explores two aspects of the relationship between the "constitution" of the EU and member states' constitutions -their potential for conflict, and possible elements of structural convergence. He considers the "constitutionalisation" of the EU as a starting point, as an on-going process, and as a desired result. The development of an autonomous institutional structure of the EU since the 1980s is presented, preliminarily culminating, after the failure of the Constitutional Treaty, in the explicitly non-statelike concept of the Lisbon Treaty. The author discusses the notion of "constitution" in a number of senses -formal vs. material, static vs. functional etc., and concludes that the potential conflict between the autonomy of EU law and the sovereignty of Member States is existential and cannot be resolved by legal means, which puts the national judge under a permanent challenge as he is obliged to serve two masters, EU law and national law. However, there is room for constructive coexistence of the two legal orders, and if considered as "non-momentary" constitutional systems "without an a priori claim of logical consistency" there is scope for mutual interaction -be it in a positive, "cross-fertilising", or a negative, intruding way, and even convergence.