Supposing that the UE economic conditions remain as the actual ones during the next years, there will be, besides the Euro introduction, even the enlargement towards the East. It is important to wonder if this enlargement will comport an increase or a reduction of the inner UE economic cohesion. This study gives a first possible answer to this question by the analysis of the economic "convergence" using non-parametric methods (stochastic kernel). Those methods will be firstly applied on the data of per capita GDP (expressed in PPS) of the actual European regions of EU-15, then they will be applied on the enlarged EU future set-up . The result of this analysis is a further tendency to polarisation, which is a worrying aspect that should encourage a new reinforcement of the structural and cohesive policies of the UE.