Research on open innovation has not yet built a comprehensive conceptualisation on how innovation intermediaries help small and medium enterprises (SMEs) in their capability development. In this paper we analyse the role that innovation intermediaries play in supporting SMEs in their international growth. We based our analysis on explorative case studies on 24 Italian firms that participated in an international program organised by UCLA. Results show that, thanks to the role played by a university intermediary, SMEs have been able to quickly learn new strategic management competences and to overcome 'local search' in their access to new market knowledge. This learning process follows different patterns in entrepreneurial and managerial firms. In raising this evidence, the paper provides a novelty contribution to open innovation studies as it describes how innovation intermediaries facilitate SMEs' international growth by facilitating their access to market knowledge in foreign countries.