In the 1970s, Western European countries were hit hard by terrorism, especially by international terrorism that crossed borders easily and allowed terrorists of different origins to carry out attacks against both governments and people. Consequently, the necessity of fighting this menace also extended to international organisations. This article looks at how the Council of Europe dealt with the issue, and assesses the negotiations that led to the Convention on the Suppression of Terrorism from the German perspective. West Germany was very interested in establishing a sounder international legal framework against terrorism and thought that the Council of Europe would be able to make an important contribution by abolishing the political offence exception that had so far been a core feature of most extradition treaties. This clause allowed political criminals to escape punishment by fleeing to a country that would deny extradition to a different country on the grounds of the political nature of the act committed by the person in question. The article gives an account and analysis of the complex negotiations that finally resulted in the adoption of the Convention in 1977, as well as of the problems encountered and compromises reached during these negotiations.