A-national principles discussed in this thesis mean broadly the principles whose origins and formation have no direct connection with any particular states by contrast with national laws. They include the general principles of law, the new lexmercatoria together with amiable composition. Within the present framework, arbitration draws upon national laws, by reference to which, questions as to whether and to what extent arbitration agreements and awards will be enforced are answered. The validity of the choice of a-national principles also has to be determined under the laws of the states connected with the arbitration. This is evident where arbitrators have to reach their decision on the basis of a specific national law in accordance with the laws of the countries connected with the dispute. Thus, the parties' freedom to select the proper law may be incompatible with the provisions of domestic laws. The application of a-national principles is controversial. However, this thesis will not examine the arguments for or against such an application. Its main aim is to examine the practice of applying a-national principles and the sometimes hostile reception this receives in national courts. Whether this can be sufficiently accommodated by the existing theories of arbitration will also be examined. Part One of this thesis, a background study, highlights the changes in the traditional three-step rule on choice of law on contract in international commercial arbitration. Part Two presents the result of the study of ad hoc and ICC arbitral awards which shows that a-national principles are increasingly applied in such arbitration. Using comparative analysis, Part Three examines the diverse attitudes held by different national courts which are in different regions and at different stages of development in the area of such arbitration. Part Four examines the conflict with the existing theories of arbitration and suggests a new approach that corresponds more closely with the application of a-national principles and the development of arbitration in an international commercial context.