Climate change stresses the importance of exploring the genetic adaptation of plants to an increase of both temperature and water deficit. To this end, dense swards of Mediterranean and temperate cultivars of Dactylis and Festuca were seed harvested after 2 years under artificial climate scenarios (range of summer drought) in two environments (Mediterranean and temperate). To assess possible genetic changes, all populations of the next generation were assessed and compared with their parent population having not been subjected to these climate scenarios. The experiment was a spaced plant design in the temperate location. The results showed that a drought escape strategy through earlier heading time and reduced total plant yield was enhanced by scenarios of greater summer drought. However, the direction and the intensity of the response of the main measured traits suggested that the physiological plant adaptation to water stress differs between species. In Dactylis, the phenology appeared to be a very responsive trait in the late heading temperate cultivar and induced a plant size reduction, while no genetic variability seems to be still available for selection within the early flowering Mediterranean cultivar. By contrast, the balance between both traits was not found so crucial in Festuca which suggests a possible greater role of the rooting system in drought resistance for this species.