The research work discusses the issue of the maintenance of contact with children in the context of the new Brussels IIb Regulation. The Regulation introduces a number of important innovations that will make it easier to resolve international divorce cases and to ensure that the rights and best interests of the child are respected. The study highlights the provisions of the Regulation, with particular attention to the issue of recognition and enforcement of foreign judgments in the context of national family law. Finally, a recent decision of the Hungarian Curia is presented, which is an important precedent in the context of the enforcement of the right of access.