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Heat and cold waves may have considerable human and economic impacts in Europe. Recent events, like the heat waves observed in France in 2003 and Russia in 2010, illustrated the major consequences to be expected. Reliable Early Warning Systems for extreme temperatures would, therefore, be of high value for decision makers. However, they require a clear definition and robust forecasts of these events. This study analyzes the predictability of heat and cold waves over Europe, defined as at least three consecutive days of Tmin and Tmax above the quantile Q90 (under Q10), using the extended ensemble system of ECMWF. The results show significant predictability for events within a 2-week lead time, but with a strong decrease of the predictability during the first week of forecasts (from 80 to 40% of observed events correctly forecasted). The scores show a higher predictive skill for the cold waves (in winter) than for the heat waves (in summer). The uncertainties and the sensitivities of the predictability are discussed on the basis of tests conducted with different spatial and temporal resolutions. Results demonstrate the negligible effect of the temporal resolution (very few errors due to bad timing of the forecasts), and a better predictability of large-scale events. The onset and the end of the waves are slightly less predictable with an average of about 35% (30%) of observed heat (cold) waves onsets or ends correctly forecasted with a 5-day lead time. Finally, the forecasted intensities show a correlation of about 0.65 with those observed, revealing the challenge to predict this important characteristic.