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The Collaborative International Dictionary
Private international law

Conflict \Con"flict\, n. [L. conflictus a striking together, fr. confligere, -flictum, to strike together, to fight: cf. F. conflit, formerly also conflict. See Conflict, v.]

  1. A striking or dashing together; violent collision; as, a conflict of elements or waves.

  2. A strife for the mastery; hostile contest; battle; struggle; fighting.

    As soon as he [Atterbury] was himself again, he became eager for action and conflict.
    --Macaulay.

    An irrepressible conflict between opposing and enduring forces.
    --W. H. Seward.

    Conflict of laws, that branch of jurisprudence which deals with individual litigation claimed to be subject to the conflicting laws of two or more states or nations; -- often used as synonymous with Private international law.

    Syn: Contest; collision; struggle; combat; strife; contention; battle; fight; encounter. See Contest.

Wiktionary
private international law

n. (context international law English) the law administered between persons of different nations.