This paper investigates the relative importance of cost, demand, financial and monetary shocks in driving real exchange rates in four CEE countries over 2000-2018. A two-country New Keynesian open economy model is used as a theoretical framework. In the empirical part, a Bayesian SVAR model with Markov switching heteroscedasticity is employed. The structural shocks are identified on the basis of volatility changes and named with reference to the sign restrictions 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 amplify exchange rate fluctuations stemming from real shocks. Third, even though the exchange rate gaps change over time, they remain quite similar across CEE countries except for Slovakia. Fourth, Slovakia introduced the euro at the time of a relatively large real overvaluation, which subsided after a lengthy adjustment process.