Some jurists prefer to call this subject matter of law conflict of laws.
In some cases, a state will defer to the laws of another, in whole or in part, in order to resolve a dispute where some element of the case commands that referral. The rules of law governing that analysis are known as private international law, international private law or the rules of conflict of laws.
In the aptly-named International Private Law or The Conflict of Laws by W. N. Hibbert (London: University of London Press, 1927), the author uses these words to define international private law:
"The body of principles determining which of two or more systems of law shall prevail when they compete in any particular case....
"The word 'private' indicates that it is the law dealing with the relations of individuals to each other, and the term 'international', that it deals with the laws of different nations."
By "individuals", it is thought that the author unintentionally omitted corporations and should of used the word persons.
In International Law, Am. Jur. 2d, page 374:
"Private international law has been defined as law directed to resolving controversies between private persons, natural as well as juridical, primarily in domestic litigation, arising out of situations having a significant relation to more than one state."