The paper presents an analysis of market power in the output milk-processing market. In particular, the paper identifies market failures in the output milk-processing market in 24 EU member states. The analysis is based on a mark-up model and the application of stochastic frontier methodology. The results show that market failures are pronounced on the EU output milk-processing market. However, the abuse of oligopoly market power is not large on average, despite the fact that we can find significant differences among the countries. The mark-up distribution is skewed toward lower values. That is, the majority of companies are characterized by only a small or almost no degree of market power; however, there are companies (about 10 %) with considerably high oligopoly market power.