The EU’s Eastern enlargement and Russia’s return to the international scene at the beginning of the 2000s meant that both actors also sought influence over the countries in their ‘shared neighbourhood’. There is broad consensus that the competition between Russia and the EU over influence in Eastern Europe and the South Caucasus is one between two actors that differ significantly in their nature and, therefore, their foreign policy approaches. This thesis subsumes the separate theorisations under more generic terms and concepts and renders EU and Russian modes of influence comparable for empirical analysis. It develops a comprehensive conceptual framework of hegemonic power in shared neighbourhoods based on three ideal-typical mechanisms of hegemonic influence: coercion, prescription, and co-optation. To exemplify the analytical value of the proposed framework and understand the nature of EU and Russian hegemony in the region, I compare the uses of the three mechanisms by Russia and the EU towards Moldova and Armenia since the beginning of the 2000s. This comparative case study was conducted using a mixed method of data analysis and collection, using official documents, press publications, interviews, observations, survey data, and statistics, thereby capturing important nuances in the informal use of foreign policy instruments. Through concept building, it contributes to the debate on regional powers in shared neighbourhoods, shedding light on the similarities and differences of the mechanisms employed by both actors.