The article concentrates on the impact of selected aspects of governance - the level of autonomy and the involvement of stakeholders in the internal governance of a university - on the research performance of universities measured by indicators of international university rankings in cross-country comparisons. The analyses are geographically situated in Europe. They follow two paths which are from the theoretical point of view based on the concepts of the principal-agent problem and stakeholder theory. Using linear regression, the author identifies statistically significant aspects of governance and compares them with results of previous studies. The findings serve as a basis for a discussion regarding how to create appropriate conditions for universities in order to improve their prospects for international success in research. The limitations of the results relating to the data, methodology and their application in the European context are discussed and general recommendations are formulated.