Understanding how power asymmetries arise and how they can affect policy outcomes are crucial questions for ecosystem services (ES) research. In political sciences and sociology, the distribution of power among individuals has been widely studied with social network analysis (SNA). SNA have also been used to understand natural resource governance, for example in the context of fisheries, REDD+ or urban green areas. This paper specifically aims at identifying who are the stakeholders who exert power over others in action arenas related to ES governance, on whom they exert their power, and what are the consequences in terms of conflicts. We propose an easily replicable method to analyze power distribution using tools from social sciences, such as interviews and workshops. We apply this method to the Mariño watershed in the Peruvian Andes considering a set of eight ES. We explicitly consider two dimensions of power: influence and domination. First, we quantify individual domination and influence scores using network degree centrality. Second, we analyze power distribution between stakeholder groups (such as sector or level of intervention) using student t tests, Clopper-Pearson exact confidence interval and chi-squared test with standardized residuals analysis. Third, we apply the quadratic assignment procedure (QAP) to explain the existence of (i) influence and domination relationships and (ii) conflicts between stakeholders. Our work provide a comprehensive assessment of power asymmetries in the governance of ES. We found that the business sector was much less influential than other actors regarding ES governance, while public sector showed higher scores of domination. We highlighted the importance of domination in the existence of conflicts between actors, and the limited effect of influence. More interdisciplinary research at the frontiers of political sciences and sustainability science is needed to understand power issues in the governance of ES.