Solidarity as one of the main values of the European Union is also recognizedamong the guiding principles of the EU asylum policy. In the period of the migrationcrisis, this principle was the most important for the EU Member Statesand very difficult to implement. The purpose of this article is to analyze the concept of solidarity, as enshrined in the Lisbon Treaty, as well as in the positions of the Member States and EU institutions. The article highlights the current debate, initiated by the Visegrad group under the Slovakian Presidency in the Council, around the proposed “flexible” or “effective solidarity” in asylum policy. Thus, the author contributes to understanding the ways, problems and prospects of refugees’ relocation, as well as the upcoming reform of the Dublin system. Based on the study of the summits conclusions, Council meetings in its various formats, the EU leaders’ statements, the author considers that divergence not only of the Member States positions, but also those of the EU institutions on the specific forms of participation in managing migration and asylum could entail more fragmentation and differentiation within the Union. At the same time, the author reveals the contradiction in the Visegrad countries’ position: while dreaming about re-nationalization of asylum and engaging in confrontation with the Commission the CEE countries by no means intend to introduce and maintain border control within the Schengen area.