There are many possible reasons for controlling market power. While in the United States the efficiency argument appears to have prevailed1, in the EU Treaty motivations such as political freedom are seen side by side with consumer welfare. Whatever the objective being pursued, it is undeniable that the laws of most industrialised jurisdictions seek, if not to constrain market power, to prohibit abuse or exploitation thereof. This article analyses, in particular, the EU approach to market power, the evolution of the assessment of market power and the levels thereof which cause the authorities to analyse the effects of a firm’s behaviour. Measurement of market power has been undergoing some changes in the EU and these are reviewed.2 The measurement of market power by the US authorities is also considered and compared to the approaches taken by the EU authorities.