Primacy
Primacy means that which comes first.
EU law has primacy, and therefore prevails, over national law. Although this it was not determined by the founding fathers of the treaties, it was recognised in revolutionary court decisions from 1963 and 1964 – the van Gend&Loos/NL and Costa/Enel cases.
This is analogous to the superiority of federal law over provincial or local state law in states like the USA, Canada, India, Germany, or Russia.
In 1970, the EU Court decided explicitely that EU law also prevails over national constitutions (Internationale Handelsgesellschaft case).
This principle has still not been accepted by most national high courts. For example, the German Constitutional Court in Karlsruhe does accept the principle in general, but when fundamental rights in the German constitution are touched upon, it calls for equivalent European fundamental rights.
The German Constitutional Court also require the right to control the limits of EU competencies. The Danish High Court took a similar decision in its verdict on the Maastricht Treaty.
30 June 2009 the German Constitutional Court went a step further in a radical verdict on the Lisbon Treaty insisting on national sovereignty for key policial areas and the right for the German Court to control the European institutions including the EU Court. See German Constitutional Court case.
This principle of primacy was explicitely inserted in Art. I-6 of the EU Constitution which was moved to a footnote in Declaration no 17 to the Lisbon Treaty.
There is a potential conflict because no single member state, except Ireland, has explicitly accepted the primacy of EU law over its own national constitution. The Irish Constitution contains the principle of primacy of EU law in its Art. 29.4.10. and repeat it explicitely in its law to ratify the Lisbon Treaty.
France, Germany, Finland and Portugal mention the EU in their constitutions, but do not accept primacy of EU law over their constitutions.
In 2013, the EU Court also decided that the Charter of fundamental rights have primacy over fundamental rights in the national constitutions when EU laws are implemented. See the Melloni case.