This paper considers cost-reducing R&D investment with spillovers in a Cournot oligopoly with minority shareholdings. We find that, with high market concentration and sufficiently convex demand, there is no scope for cross-ownership to improve welfare regardless of spillover levels. Otherwise, there is scope for cross-ownership provided that spillovers are sufficiently large. The socially optimal degree of cross-ownership increases with the number of firms, with the elasticity of demand and of the innovation function, and with the extent of spillover effects. In terms of consumer surplus standard, the scope for cross-ownership is greatly reduced even under low market concentration.