The effective response to the proliferation and growing diversity and sophistication of cyber threats requires a broad spectrum of competencies, human, technological and financial resources that are in the powers of very few countries. The European Union is addressing this challenge through an initiative to establish one or more cybersecurity competence networks. A number of existing technologies can support collaboration in networked organisations; however, network governance remains a challenge. The study presented in this article aimed to identify and prioritise network governance issues. Towards that purpose, qualitative and quantitative methods were applied in the analysis of norms and regulations, statutory documents of existing networks, academic sources and interviews with representatives of funding organisations and potential major customers. The comprehensiveness and complementarity of these primary sources allowed to identify 33 categories of governance issues and group them in four tiers, indicative of the respective priority level. The results of the study are currently used to inform and orient the development of alternative models for governance of a cybersecurity network and a set of criteria for their evaluation. They will support informed decision-making on the most appropriate governance model of a future networked organisation, evolving from a project consortium.