A: I try to answer questions as simply as possible. Regrettably, this question is very, very complicated.
The short answer is that non-U.S. citizens working for U.S. companies who are injured in a maritime accident may be able to bring legal claims against those companies under U.S. maritime law or the Jones Act, which, as a general matter, are considerably more favorable than the law of other countries.
However, there are some situations where U.S. maritime law will not be available. In these cases, you may be looking at international law, international arbitration, or the law of some other country.
I would strongly, strongly recommend that you retain the services of an attorney who understands international maritime injury law. There are not many attorneys who really understand these cases, so make sure you carefully research and questions your attorney before hiring him or her.