Environmental co-management has been advocated and applied in diverse contexts as an integrative and inclusive approach to make biodiversity conservation more effective and contextual. Co-management however requires the actors involved to overcome tacit boundaries and reconcile different viewpoints to reach a shared understanding on the environmental problem and envisioned solution(s). We depart from the assumption that a common narrative can serve as a base for a shared understanding and analyze what types of actor relations in co-management influence the emergence of a common narrative. Empirical data is collected using a mixed-method case study design. We apply the idea of narrative congruence, which relates to the similarity of narrations that actors tell, to investigate the effects of the types of relationships between two actors as well as specific leadership roles using an Exponential Random Graph Model. We find that frequent interaction between two actors and a trusted leader with many reciprocal trust ties to be important drivers to support the emergence of narrative congruence ties. Connecting leaders, i.e. actors in brokering positions, show a statistically significant negative correlation with narrative congruence ties. The results suggest that a common narrative tends to emerge in sub-groups around a highly trusted leader, in which actors talk frequently to each other. A brokering leader, however, seems to face strong difficulties of forming narrative congruence ties with others, although such brokers may play central roles in the co-design of common narratives to form the basis for motivating collective action in co-management. Lastly, we discuss the importance of common narratives and how leaders can better succeed in co-designing these in environmental co-management approaches.