This paper aims to analyze to the regulation of the family matters in the EU “acquiss communautaire” regarding marriage, dissolution of marriage, marital property regimes and parental responsibility. The European Union law of these recent years has shown some increasing trend of intervening in the regulation of family relationships. Community acts in the area of family law are the acts for the recognition of the foreign judicial decisions and for the jurisdiction criteria as well as finally the uniform conflict rules, but no material acts. Thus, this is about rules which exclusively regulate only the international cross-border family matters, leaving unregulated the core of the family matters. The regulation of these cases aims to create, maintain and develop a common area of freedom, security and justice, with a view to the well functioning of the common European market. In accordance with the power provided by the EU Treaty, the European Commission has adopted the Regulations Brussels II bis and Rome III. Also the paper will focus in the study of the institute of marriage and parental responsibilities in the cases of marriages with foreign elements, seen in the framework of the new Albanian Act “On private international law” compared to the previous law and compared with the EU regulations Brussels II bis and Roma III.