It is disputed, whether non-national or transnational law rather than the law of a state, e.g. Swiss law, can be the applicable law in international commercial arbitration, and therefore, if non-national lex mercatoria can be the sole applicable law in International Commercial Arbitration. Even more controversial is the question if Arbitral Tribunals can elect to apply non-national law if the underlying arbitration agreement does not provide for an applicable law or is unclear with regard to this matter. It is considered uncertain whether there will be a solution to this question, despite the fact that as early as at its 1992 meeting in Cairo the International Law Association recommended to give such a competence to Arbitral Tribunals. In this short paper we will look at the pros and cons regarding such a competence of Arbitral Tribunals to decide on their own which law to apply if neither the arbitration agreement nor the domestic law applicable in the seat of the tribunal provides for a solution. In developing an approach, we will look at a parallel aspect from an other field of international law in order to shed light on the current state of the law on this question and to define its relation to domestic rules already in place. At first we will look at the legal situation within the UNCITRAL Model Law and in several jurisdictions which have been chose according to the importance of the respective states' economies for international trade. Arguments in favor for a wide competence will be brought to the readers' attention as well as arguments against it with a special look at CISG before a conclusion is drawn based on the current situation, the arguments heard and the needs of the parties involved.