This paper attempts to determine whether or not nominal exchange rate regimes affect the volatility of bilateral and effective real exchange rates. To that end, we examine the real exchange rate behaviour for a set of OECD and non-OECD countries during the 1960-2006 period, therefore covering both the Bretton Woods system of fixed exchange rates and adoption of generalised floating exchange rates from 1973. We make use of an econometric methodology based on the Hansen (1997)'s approximation to the p-values of the supreme, exponential and average statistics developed by Andrews (1993) and Andrews and Ploberger (1994). This methodology allows us to obtain a profile of pvalues and to delimit periods of stability and instability in the variance of real exchange rates. Results suggest that there is clear evidence in favour of the non-neutrality of nominal exchange rate regime regarding real exchange rate volatility for developed countries, but not in the case of developing or emerging countries. JEL Classification Numbers: F31, F33, F41