The latest research and development (R&D) framework programmes of the European Union (EU), “Horizon 2020” and “Horizon Europe”, have significantly increased the resources available to promote science and innovation in Europe. However, the strong competitiveness of the research teams and their search for excellence may cause inequality in the spatial distribution of investment effort in R&D. The aim of this paper is to analyse the geographic distribution of R&D spending in the EU. A greater concentration of funds is observed in the most advanced and dynamic economies, capable of promoting more competitive research teams and projects. Through an empirical analysis, estimated by a spatial convergence model, it is found that EU R&D funds are preventing cross-regional convergence in Europe by driving growth mainly in wealthier regions. Based on these results, it seems relevant to consider spatial correction mechanisms for the distribution of R&D resources so that they achieve greater territorial cohesion in Europe.