The article outlines the conception of a multi-centric system of law based on a situation where in the territory of a state the law of given state, the EU law and the law created on the ground of the European Council apply simultaneously, which may result in the existence of contradictory valid and final court decisions. The multi-centric understanding of the system of law exceeds the traditional tension between legal positivism and iusnaturalism. The multi-centric system of law tends to the network configuration, but its subsystems retain their hierarchic structure. The article applies the multi-centric understanding of the system of law, especially to the relationship between the legal order of EU and legal orders of the individual member states, from the view of the European Court of Justice and the Constitutional Court of Poland. The latter bases its doctrine of their relationship on the principles of mutually favourable interpretation, cooperative application. The principle of the interpretation favourable for the European law is however limited. It cannot lead to results which are contrary to the explicit wording of the constitutional rules. In the principle of precedence of the EU law two levels of cogency and application may be distinguished. At the first level the precedence of the constitutions of the member states may be accepted, which will retain their decision-making at the moment of potential collision of EU rules with their own rules. In case of the application of the law the precedence of the EU law, resulting from the principle pacta sunt servanda contained in the Polish Constitution, comes to the foreground, thus the EU law has the application precedence under the Polish Constitution after all.