International and national courts have sometimes disagreed as to whether national law is the primary law that applies to a dispute. The differences do not seem to be due to the territorial or international nature of the tribunals. In ICSID, for example, the tribunals have ruled that national law should be applied on its merits. It should be noted, however, that such differences are very rare. So, it might be best to rely on national law in a case, rather than international law.
The relationship between international and national law is often framed as a clash between dualism and monism. Dualism emphasizes the distinct nature of the two legal systems, and argues that international law applies to national law only in part. This approach is inconsistent with the fact that neither legal system is created by the other. However, this is not to say that both systems cannot influence one another. Rather, it is possible to recognize international law in part and use it as a guide when interpreting a law in a particular country.
When the conflict arises in a foreign country, international law will likely apply. The ICSID Convention provides for recourse to international principles and rules when a country fails to apply a specific rule. However, this is not always possible. Instead, the tribunal would first verify that the national law fails to address the issue. Then, it could apply international law to cases where it conflicts with a specific national law. This is a particularly complicated situation because it requires the tribunal to determine if the national law is insufficient.