Responsible Research and Innovation (‘RRI’) is a cross-cutting priority for scientific research in the European Union and beyond. This paper considers whether the way such research is organised and delivered lends itself to the aims of RRI. We focus particularly on international consortia, which have emerged as a common model to organise large-scale, multi-disciplinary research in contemporary biomedical science. Typically, these consortia operate through fixed-term contracts, and employ governance frameworks consisting of reasonably standard, modular components such as management committees, advisory (...) boards, and data access committees, to co-ordinate the activities of partner institutions and align them with funding agency priorities. These have advantages for organisation and management of the research, but can actively inhibit researchers seeking to implement RRI activities. Conventional consortia governance structures pose specific problems for meaningful public and participant involvement, data sharing, transparency, and ‘legacy’ planning to deal with societal commitments that persist beyond the duration of the original project. In particular, the ‘upstream’ negotiation of contractual terms between funders and the institutions employing researchers can undermine the ability for those researchers to subsequently make decisions about data, or participant remuneration, or indeed what happens to consortia outputs after the project is finished, and can inhibit attempts to make project activities and goals responsive to input from ongoing dialogue with various stakeholders. Having explored these challenges, we make some recommendations for alternative consortia governance structures to better support RRI in future. (shrink)