Opportunities may arise to arrest a ship in maritime zones beyond internal waters, e.g. in the territorial sea and the exclusive economic zone (EEZ). This paper examines the possibilities for arrest in those areas on the basis of jurisdiction ratione loci and ratione materiae. Under Belgian law the territorial sea is not part of the State's territory; accordingly, the Belgian Judicial Code does not provide for an attachment judge nor a bailiff to have jurisdiction in this area and a fortiori in the EEZ. The law of April 22, 1999 solved the problem of territorial jurisdiction in this respect. As far as a ship's arrest in the EEZ is concerned, it is not clear whether the United Nations Law of the Sea Convention (articles 73 and 220) combined with the requirement of a maritime claim, allows for an arrest at all.