The economic and social cohesion policy of the European Union has two inter-related components, namely the vertical cohesion, referring to the alleviation of social disparities and the solidarity with the disadvantaged social groups, and the horizontal cohesion, which concentrates on the regional disparities decrease and the solidarity with the lagging regions' population. Based on this approach, the EU's regional policy is closely related to the horizontal dimension of the cohesion policy and is supported by the EU funds via allocations for convergence - competitiveness and employment - European territorial co-operation objectives of the 2007-2013 programming period. The Central and East European Countries, as New Member States (NMS) of the EU are a major beneficiary of these allocations, especially with regard to the convergence objective, considering the big regional disparities they display in comparison with the EU average. At the EU level it is largely acknowledged that transition to the market economy experienced by these countries has deepened the regional disparities; at present the main issue is when and with which rate a process of regional convergence will occur, both inside each country and compared to the EU average. Hence, the main questions this paper raises: first, which are the implications of the cohesion policy, via EU funds for regional disparities in the NMS? Second, are these countries prepared to ensure a high capacity of absorbing the EU funds and, thus, to turn to good account their endogenous growth potential? In order to answer these questions empirical evidence based on the EU statistical data and studies will be provided, accompanied by comments upon the so-called 'absorption problems'.