How should competition law deal with anti-competitive behaviour by firms with market power? In the light of recent EC and US cases, this is perhaps the most controversial current issue for competition policy. Lax policy would jeopardise the competitiveness of markets, but rigid policy would chill pro-competitive, pro-consumer conduct. This paper gives an economic assessment of evolving legal standards in the area. The importance of developing a stronger economic basis for EC law on abuse of market dominance is stressed.