The enlargement of the European Union is an almost everywhere accepted necessity, but at the same time of course also a compromise. Economies or regions of different economic, social, institutional, etc. development become united in Europe with a territory from the Atlantic to the Eastern borders of Poland, Slovakia and Hungary, from the Baltic Sea to the Mediterranean Sea. This integration process going along with the worldwide globalisation will imply a new distribution, or a redistribution of the factors of production. First of all the human capital will be touched by this development.2 One of the most important results found by social sciences in the 20th century is the realisation of the immense role played by human factors in the process of economic development. The extremely high efficiency of human capital and the high mobility could diminish the regional differences in the economic development and therefore in the social life. But even this is one reason for the mentioned re-allocation of the human capital. In the frame of a very simple static model (See e. g. Bishi – Kopel [2002]) the flow of human capital between different regions – called the European Union and the New Member States – will be analysed. The introduction of search costs extends the field of policy-analysis.