The author gives an overview of case law of the European Union on the issue of competition - cartel in a member state, which began before the accession of that state to the European Union - Article 81 EC and Article 53 of the EEA Agreement - definition of powers and jurisdiction of the commission and national competition authorities - the principle of ne bis in idem - Regulation (EC ) No 1/2003 - Article 3, paragraph 1 and Article 11 odst.6 - consequences of the accession of new member states to the union.