The crises of the XXI century made the reflections on the solidarity and unity of the EU urgent again. The research aim is to explore the application of two notions, namely the European Union and Europe for two striking cases, namely the UK and the Visegrad states positions on the issues of European integration. These countries are geographically the peripheral states of the European Union and, therefore, they may be examined under the general philosophical approach to the dichotomy between the core and the periphery. This approach provides for suggestions that taking into account recent difficulties the EU has been facing, the EU periphery has escaped the control of the core that is the status gained by Brussels (the UK case) or has tried to weaken the core (the Visegrad states case). The migration factor that is still very urgent serves not exactly the cause but the manifestation or the proof of the periphery instability. Brexit was the starting point for the UK to separate the notions of the European Union and Europe that seemed to have merged as synonyms. The case shows that the EU notion has narrowed, while on the contrary the importance of Europe as the region not limited to the EU has increased. The case of the Visegrad countries demonstrates that despite the ambiguous attitude of the population and political elites to the EU, these states are unlikely to follow the UK scenario in the short term. At the same time the group displays sustained euroscepticism and considers itself to be an alternative but not equal, though, format of integration in Europe. Taking into account the existing distance between the European values and European institutions (presented by the EU), the Visegrad group may be considered not only a potential troublemaker in the dichotomy between the core and the periphery during the crises in the EU, but also the group of states that considers itself to have the right to behave in its independent way without following completely the instructions from Brussels. The authors conclude that the countries at the periphery of the European Union are unlikely to consider the EU and Europe as equal notions. The countries of the EU periphery are striving for their unique place and cooperation format that may not coincide with the EU. None of them deny being European instead aiming at proving their Europeaness both inside and outside the EU. However, the UK may find its place outside the EU while it is more difficult for the Visegrad group countries that do not seem to have any viable alternatives.
