The relationship between market structure and performance has been studied extensively for American banking. In contrast, little work has been done to investigate this relationship for European banking. Two explanations of a positive correlation between profitability and concentration have been advanced, the traditional structure-performance hypothesis (SCP) and the efficient-structure hypothesis. Previous empirical tests of the alternative hypotheses have yielded mixed results but the tests were not robust because they did not incorporate measures of efficiency directly in the model. This study applies a stochastic cost frontier as proposed by Aigner et al. (1977) to derive measures of X-inefficiency and scale-inefficiency, under the assumption that the errors are distributed half-normal. We incorporate these measures of inefficiencies directly into the tests as proposed by Berger and Hannan (1993). We do not find a positive and significant relationship between concentration and profitability for a sample of banks across 11 European countries over a four year period, 1988-91. However, we do find evidence to support one of the two versions of the efficient-structure hypothesis for banks located in countries with low concentration of banks. Since little support is found for either of the SCP hypotheses, a simple policy of strict limitations on cross-border acquisitions and growth is not warranted.