Each vessel normally flies the flag of the owner's country. That means it is registered in the national register of that particular country. Flagging in is the process of adding a vessel to the national registry and "flagging out" is the process of removing a vessel from a national registry. Generally flagging out refers to the practice of switching the vessel's registration to another country to fly operate it under a "flag of convenience". However, some vessels that have been deleted from national registries end up operating under no flag at all.
