Extremes are assessed here in an attempt to validate the two French models in their representation of the second part of the 20th century, using different sources of gridded observational datasets. Models show some ability to simulate extremal behaviour of the climate even if discrepancies are noticeable between models and observations. These may be partly due to the low resolution used for the present study simulations. Extreme indices, calculated using the STARDEX (STAtistical and Regional dynamical Downscaling of EXtremes for European regions) methodology, are investigated in different IPCC (International Panel on Climate Change) scenarios performed by the French community. Investigation of 21st century severe indices simulated in these simulations shows some interesting features. In some parts of the world, extreme temperatures experience a more rapid increase than the mean, suggesting that the Power Density Function (PDF) may not only be shifted toward higher temperatures but also changed in its shape. Extremes of precipitation also experience a change toward more intense precipitation events in winter and longer dry events in summer. Approaching future changes in extreme indices through their relationship to mean annual temperature may be a useful approach in multi-model studies, since it provides a measure of the sensitivity of extremes to warming conditions in these models.