We assess the sustainability of external imbalances for EU countries using panel stationarity tests of Current Account (CA) balance-to-GDP ratios and panel cointegration of exports and imports of goods and services, for the period 1970Q1–2015Q4. We find that: i) the country panel is non-stationary; ii) cross-sectional dependence plays an important role; iii) there is non-stationarity of the CA, imports, and exports with cross-sectional panel dependence and multiple structural breaks; iv) however, there is a stable long-run relationship between exports and imports in the panel. Hence, trade imbalances can be less unsustainable but this is not sufficient to make current account imbalances sustainable.