This paper investigates the relative importance of cost, demand, financialand monetary shocks in driving real exchange rates in four CEE countries over2000–2018. A two-country New Keynesian open economy model is used as atheoretical framework. In the empirical part, a Bayesian SVAR model withMarkov switching heteroscedasticity is employed. The structural shocks areidentified on the basis of volatility changes and named with reference to the signrestrictions derived from the economic model. Main findings are fourfold. First,real and financial shocks have similar contributions to real exchange variability,whereas that of monetary shocks is small. Second, financial shocks amplifyexchange rate fluctuations stemming from real shocks. Third, even though theexchange rate gaps change over time, they remain quite similar across CEEcountries except for Slovakia. Fourth, Slovakia introduced the euro at the timeof a relatively large real overvaluation, which subsided after a lengthy adjustmentprocess.