This thesis takes a look at Austrias competence in cross-border circumstances. Because of the increasing cases of parental custody with cross-border relations, some contracts with regard to jurisdiction, recognition and execution have been signed. Especially the new Brussels IIa-Convention, the Hague Convention on the Civil Aspects of International Child Abduction, the Convention concerning the Powers of Authorities and the Law applicable in Respect of the Protection of Infants and the European Convention on Recognition and Enforcement of Decisions concerning Custody of Children and on Restoration of Custody of Children are relevant and are going to be examined in detail. The regulations of jurisdiction are going to be investigated and will give an overview, in which cases Austria is competent and in which case, which convention is relevant. The norms, concerning the jurisdiction, are going to be explained on the basis of examples. In particular the Brüssel IIa-Convention, which became effective in 2003, brings a lot of innovations in the field of parental custody, which also has an effect on the other mentioned conventions.