The article briefly describes international legislation in parental responsibility matters and focuses on the Council Regulation (EC) No 2201/2003 of 27 November 2003 concerning jurisdiction and the recognition and enforcement of judgments in matrimonial matters and the matters of parental responsibility, repealing Regulation (EC) No 1347/2000 (in practice called Brussels II a or Brussels II bis). The essay reveals and analyses the difficulties which occur while hearing parental responsibility cases within the European Union. Particular attention is given to special cases which were difficult to resolve for the national courts of the Republic of Lithuania. Also, the practice of the Court of Justice of the European Union is examined. The guidelines on how to avoid the problems of establishing jurisdiction are given. The relations of 1980 Hague Convention on international child abduction and Regulations Brussels II bis are revealed and the reasons for adoption of the Regulation are highlighted. The article also proposes improvements for Article 15 of the Regulation and the effective application of a modified forum non conveniens doctrine in parental responsibility cases.