This - if I may say so - internal "exchange rate" stability aspect has often been overshadowed by the disproportionate interest in US dollar/euro exchange rate. The dollar/euro exchange rate movements have, in fact, been fully in line with the dollar's historical fluctuations vis-à-vis the European currencies prior to the introduction of the euro.
More importantly, the weight of the fluctuating part in exchange rate "baskets" is, in all Member States, now much smaller than in the past. BIS Review 93/2001  1  For example, for Austria as a small open economy the external stability of the currency was of prime concern.