This dissertation contributes to the literature addressing the euro adoption by the New Member States (NMSs) of the European Union by proposing a definition of real convergence based on real exchange rate (RER) dynamics. As fluctuations in RER represent deviations from purchasing power parity (PPP), the thesis also adds to the literature on PPP theory. Finally, by proposing basic and extended small open economy dynamic stochastic general equilibrium international real business cycle (SOE-DSGE-IRBC) models of RER determinants for the NMSs, it fills a gap that has hitherto existed in the literature. The analysis of RER dynamics is conducted on two levels: empirical and theoretical. On the empirical level, the scale of RER dynamics in the NMSs is measured. Factors contributing to these dynamics are identified. Particular attention is drawn towards the factors which could account for the recorded appreciation of RER in these countries since the early 1990s. On a theoretical level, variants of the SOE-DSGE-IRBC model of RER determinants for a typical NMS are developed. The findings of Chapter 1 show that the univariate variance analysis accurately measures real convergence in the analysed countries. The results also indicate that at present, only Estonia and Slovenia (ex post) are ready to adopt the euro. The basic SOE model of Chapter 2, unlike its expanded version of Chapter 3, is only able to roughly match the moments of the Polish data. Therefore, its findings provide insights into the theoretical ‘puzzle’ of RER volatility and its persistence. The expanded model results show that productivity shocks to the non-traded sector are the main cause of price differentials between Poland and the euro area. This is in contrast to the two competing hypotheses that either productivity or quality improvements in the tradable sector are the main source of real exchange rate appreciation in this country.