The object of this study is an analysis of the present tendencies of the requirements imposed on arbitration tribunals in Poland with respect to the law applicable to the substance of the dispute in the absence of a choice made by the parties. In 2005, Polish arbitration law (fifth part of the Civil Procedure Code) was significantly modified. One of the provisions added by the legislator – Article 1194, Paragraph 1 CPC – imposes a general obligation to settle the dispute in accordance with the “applicable law,” which might possibly be interpreted as imposing the obligation to apply international private law. The author finds, however, that such an interpretation is not supported by the Code itself nor by the present tendencies in the law of arbitration. At the level of arbitration doctrine and jurisprudence, there are two major approaches practicable with respect to the problem: the “indirect method” (application of conflict rules by the arbitrators) or the “direct method” (designation of applicable law without the use of such mechanism). Neither Article 1194, Paragraph 1 of the Polish CPC nor the other provisions of the Code are an obstacle to the application of these two methods.