This article addresses the conventional admissibility of "No International Pending Lawsuit". From a basic, descriptive and deductive research we obtain the result of this analysis, which allows us to understand the concept of international pending lawsuit; and the general goal of identifying the lines of argumentation of the European tribunal of human rights and the European commission of human rights when a state proposes the inadmissibility of the lawsuit based on an international pending dispute. As a result a international pending lawsuit takes place when there exists identity between the parties, the complaint and the facts, plus, it is filed before an international court that is public and judicial or quasi-judicial with procedures of a contentious and contradictory nature.