The aim of the article is to identify barriers and threats associated with operation of small and medium-sized enterprises on the European Union market, as well as to evaluate the ability of these entities to compete on the European market. The authors formulate a theses that in the early years of their membership there firms will have to incur sizeable expenditure on adjustment to operation on the Single European Market, which may adversely affect their competitiveness. High costs of these adjustments are bound to have, in the first place, an adverse impact on activities on the smallest companies in this sector. The article presents results of empirical research carried out in 2003 in enterprises within the framework of "The Impact of State Aid Instruments on Competitiveness of Small and Medium-sized Enterprises. Poland - European Union. A Comparative Study" (a project sponsored by the State Scientific Research Committee). It attempts to answer the question of the way in which entrepreneurs perceive their current market position and of the changes expected in that area after Poland’s accession to the EU. In addition to that, ways in which the analysed entities react to the new situation have been analysed, with special stress put on overcoming of barriers to development. The authors have also pointed out that to solve the problems due to emerge in company operation on the Single European Market will require support on the part of economic policy of the Government, including state aid instruments.