Parallel litigation of cross-border disputes has become a widespread and multifaceted problemin the field of international jurisdiction, which requires research and resolution on the level of theinternational community and at the level of individual states. The article is devoted to comparative legalanalysis of the legislation of foreign states governing parallel litigation, as well as research of relevantlaw enforcement practice. The author provides a division between the continental law approach andcommon law approach. Hence, the author examines the relevant provisions of the laws of the USA,UK, Canada, as well as the law of the EU, Switzerland, Turkey and Japan. The need in identifyingtwo common approaches is accounted for the objective principles of legal regulation of relationsarising in connection with parallel litigation. On the basis of these principles one can distinguish thefollowing two social legal values as justice and legitimacy, which to some extent dictate the logic andjustification of the application of the outlined approaches. The approach of common law countriesaimed at the most fair and effective resolution of cross-border dispute due to ability of the court toapply the doctrine of forum non convenience and to accommodate the different circumstances ofthe case to substantiate its or jurisdiction of a foreign court in respect of the dispute. Continental lawapproach, in turn, is focused on the predictability and certainty in the resolution of the question of thesuspension or on the contrary, on the refusal to suspend the proceedings in connection with parallelproceedings. The specificity of the approach of common law countries is appeared in the ability tojustify the legitimacy of parallel processes, which undoubtedly is contrary to the basic provisions ofthe continental approach according to which the parallel litigation is unacceptable. The parties tocross-border commercial relations, while planning procedural strategy even before the emergenceof the dispute, can take into account features of a particular approach in order possible use of theeffect of parallel proceedings that may occur, for example, in obtaining a speedy trial prejudicial act.In this regard, it is concluded that at the present stage of development of the rules on internationaljurisdiction there is no straightforward solution of the problem of parallel litigation.