The paper deals with the implementation of the grounds for non-execution the European arrest warrant in the Slovak Republic. It is divided into four sections. While the first section deals with the mandatory grounds, the second section deals with the optional grounds. The third section analyses their implementation in the Slovak Republic and solves the question whether all ‘Slovak mandatory grounds for non-execution the European arrest warrant’ are really mandatory. The last fourth section introduces author’s considerations lex ferenda towards Slovak Act No. 154/2010 Coll. on the European Arrest Warrant.