Resilience is a widespread concept and a key priority for the EU. We focus on resilience’s relations with stability. These notions have been subject to ongoing theoretical debate and have not been clearly separated in EU discourses. We explore how resilience and stability have been used regarding the Southern and Eastern dimensions of the European Neighbourhood Policy (ENP) and suggest how their different meanings may be better distinguished and conceptualised. Resilience has penetrated the ENP’s discourses unevenly and attracted the limited interest of the neighbours. Besides, the EU’s policies will likely face numerous practical problems mostly similar to the ENP’s both dimensions. The EU’s policies themselves have disturbed stability in its neighbourhood, and now, even restoring the old stability would be problematic, let alone attaining a more positive one. Furthermore, the EU could impose its views regarding stability and/or resilience. Also, Brussels could de facto uphold negative stability and/or resilience.