Under the nationality principle, the law of the flag applies to crimes committed on board. I don't know how these types of situations work, in practice, but federal law is very clear...
"It is unlawful for any person on board a vessel of the United States, or on board a vessel subject to the jurisdiction of the United States...to possess with intent to manufacture or distribute...a controlled substance."
Maritime Drug Law Enforcement Act. 46 U.S.C. app. § 1903
Also -- under the
Federal Controlled Substances Import and Export Act, it is unlawful for any person to possess a scheduled substance on a boat or airplane.
The courts have approved of these laws, saying that international law can only be raised as a defense if it is invoked by that foreign nation to protect a foreign ship (of same nation). (So if you were sailing and arrested on a Colombian ship, for example, the govenment of Colombia would have to object to U.S. jurisdiction.)
Also remember that U.S. customs officials may conduct border search without violating Fourth Amendment. Again, I don't know how these laws operate in practice. Most of the published opinions involve big time offenses. I've never been on a cruise. I've never talked to anyone who's been busted on a cruise. But there is probably a typical course of action for these guys.
Still, it's pretty exciting to see an admiralty question in this forum.
