This paper deals with the characteristics of the term sovereignty as well as state power. Its aim is to find out whether the sovereign position of the states is changed in terms of an era of globalization. We can demonstrate this by answering the question whether the Slovak Republic lost its sovereignty when accessing the European Union. In this paper, the accession of the Slovak Republic into the European Union and the transmission of part of its sovereignty are also mentioned briefly. The reader can find the definition of sovereignty within the interpretation of the Constitutional Court of Czech Republic, and the possibility for Member States to withdraw from the European Union. Last but not least, the article is finished with the cogitation about the power position of nation states.