Mark-ups can provide valuable information on competitive pressures in various sectors of the economy, reflecting pressures stemming from rules of conduct imposed by regulators as well as those arising from such factors as trade and FDI or increasing consumer demands in terms of price and quality. This study estimates mark-ups for services industries in European OECD members and its novelty is that it i) allows for non-constant returns to scale, ii) jointly estimates mark-ups for all sectors and in all countries and iii) estimates mark-ups at a detailed level of sectoral disaggregation. The estimation is done for the period 1993-2006 and uses firm level data of the Amadeus database. In general, the estimated mark-ups are higher for professional services, real estate, renting and utilities, while they tend to be substantially lower for construction, computer services, retail and wholesale trade and catering. There is also large variation across countries in terms of the sizes of the estimated mark-ups. Competitive pressures according to these mark-ups should be large in the United Kingdom and most Scandinavian countries, and relatively small in Central European countries, Sweden and Italy.