This paper uses the EAGLE, a multi-country dynamic general equilibrium model, to illustrate dynamic adjustments in a small open economy undergoing real convergence. We consider the effects of productivity catch-up and misperceptions about future productivity developments. Our results indicate that even if real convergence takes the form of a gradual process, the dynamic responses of key macrovariables can be far from smooth. We also find that overly optimistic expectations about productivity shifts can generate sizable boom-bust cycles and so be relevant in accounting for cyclical deviations from a sustainable real convergence path. Our comparisons across alternative monetary regimes reveal that a flexible exchange rate helps to smooth real convergence processes and misperceptions associated with tradable sector productivity, while the opposite usually holds true for scenarios based on nontradable sector developments.