According to the relevant EU regulations, as of 26 June 2012, Member States may only issue individual travel documents, thus the basic principle of one person having one document will prevail.
However, exceptionally, until 31 December 2012, Hungarian border control authorities permited entry and exit for those Slovakian children under age of 12 years, who were travelling with their parents and were registered in the parents’ passports issued by the Republic of Slovakia.
As of 1 January 2013, EU citizens, including children, must have their own individual travel documents to visit Hungary. Even after that date a parent holding passport, which contains his/her child’s data, can use the passport for his/her own travel within the validity of the document.
For detailed information on the relevant EU regulation, please visit the following website: http://europa.eu/travel/doc/index_en.htm