Computed fundamental real exchange rates in four acceding countries point out to difficulties in entering the ERM II too soon after the EU entry. Computations suggest that it is unlikely for the Czech, Hungarian and Polish economies to maintain low inflation during 2004-2010, and at the same time, to keep their currencies within the ERM II. In addition, those currencies were overvalued in 2003. Moreover, experience of Greece, Portugal, and Spain – viewed through the fundamental real exchange rates goggles - indicate both more stable paths of real exchange rates as well as smaller currency misalignments prior to the euro adoption than what can be expected from the acceding countries in the forthcoming years. If acceding countries sail too fast towards the euro, their sailing may not be as smooth as the one of frontrunners.