The study contains a step-by-step algorithm for determining the law applicable to private cross-border legal relations. The algorithm is developed based on legislation, law enforcement practice and doctrine. The initial rule of the sequential execution of the stages (steps) of the algorithm is a mechanism in which the determination of the law applicable to the legal relationship at one of the stages excludes the subsequent stages of the algorithm. Public policy interests dictate the rules for determining the law to be applied to private law relations complicated by a foreign element. The establishment by the legislator and law enforcement officer of the closest connection between the interests of conflicting public orders (legal orders) with elements of cross-border legal relations is the basis for the process regulation in the Russian Federation. At the first, second and third stages of the algorithm, the interests of the domestic public order (law and order) dominate. At the fourth stage of the algorithm, public interests in the part not regulated by super imperative norms are correlated with the agreement of the parties on the choice of the applicable law. At the fifth — eighth stages of the algorithm, the law enforcement officer is guided by the rules established by the legislator taking into account the interests of public orders that are conflicting in cross-border legal relations. At the last, ninth stage of the algorithm, the applicable law is established by the judge based on the closest connection between the interests of public order (law and order) with elements of crossborder legal relations.