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This paper develops an open economy New Keynesian model in which shocks to monetary policy generate delayed nominal exchange rate overshooting. We show analytically that delayed overshooting is a consequence of heterogeneity in nominal price rigidities. Immediately after a contractionary monetary shock, the reaction of firms with relatively flexible prices generates a strong response of inflation, alongside a currency appreciation. Overtime, as firms with relatively less flexible prices adjust, the appreciation continues, but is subsequently followed by a depreciation. In a calibrated version of the model, with heterogeneity in price rigidity matched with micro-evidence, the peak response of the nominal exchange rate to a monetary policy shock occurs at around 4 quarters.