Private international law deals with private relationships across national borders. This is also called conflict of laws in the US. Examples of private international law topics include family law matters, recognition of judgment, torts, contracts, etc.
“Private international law is the body of conventions, model laws, national laws, legal guides, and other documents and instruments that regulate private relationships across national borders. Private international law has a dualistic character, balancing international consensus with domestic recognition and implementation, as well as balancing sovereign actions with those of the private sector. United States domestic law’s nearest equivalent to private international law would be interstate “conflict of laws” or “choice of laws.””
Don Ford, Private International Law, ASIL e-RG Electronic Resource Guide, https://www.asil.org/sites/default/files/ERG_PRIVATE_INT.pdf
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