This paper is motivated by the European Union strategy to secure competitiveness for Europe in the globalising world by focussing on technological supremacy (the Lisbon - agenda). Parallel to that, the EU Commission is trying to take a more economic approach to competition policy in general and anti-trust policy in particular. Our analysis tries to establish the relationship between increasing knowledge intensity and the resulting market concentration: if the European Union economy is gradually shifting to a pattern of sectoral specialisation that features a bias on knowledge intensive sectors, then this may well have some influence on market concentration and competition policy would have to adjust not to counterfeit the Lisbon-agenda. Following a review of the available theoretical and empirical literature on the relationship between knowledge intensity and market structure, we use a larger Eurostat database to test the shape of this relationship. Assuming a causality that runs from knowledge to concentration, we show that the relationship between knowledge intensity and market structures is in fact different for knowledge intensive industries and we establish a non-linear, inverted U-curve shape.