Stress-tolerant forage resources are increasingly needed for the environmental and economic sustainability of extensive Mediterranean livestock systems. Perennial forages such as cocksfoot ( Dactylis glomerata L.) can be a valuable alternative to annuals, if they can survive across successive summer droughts. One Mediterranean cultivar of cocksfoot subsp. hispanica with complete summer dormancy (Kasbah), five non-dormant (Delta 1, Jana, Medly, Ottava) or incompletely dormant (Currie) Mediterranean cultivars of subsp. glomerata, and one Continental cultivar (Porto) of subsp. glomerata, were evaluated for dry matter yield over three years and persistence as final plant survival in six sites of Algeria, France, Italy, Morocco and Portugal, with the objectives of: (i) modeling adaptive responses and targeting cultivars as a function of environmental factors associated with genotype × location (GL) interaction; (ii) defining plant ideotypes, adaptation strategies and opportunities of international co-operation for regional breeding programmes. Adaptive responses were modeled by joint regression, additive main effects and multiplicative interaction (AMMI), and factorial regression. The most predictive models were: (i) factorial regression as a function of site spring–summer drought stress (as long-term potential evapotranspiration minus actual water available), for yield; (ii) AMMI including one GL interaction principal component related to site annual and spring–summer drought stress, for persistence. GL interaction of crossover type for yield and persistence was large and mainly associated with the summer dormancy trait. Completely dormant germplasm was specifically adapted to severe drought. Non-dormant Mediterranean cultivars tended to be specifically adapted to moderate drought stress, although they varied to some extent in adaptive response to drought-stress levels. The Continental cultivar was generally misadapted. The completely summer-dormant germplasm also tended to have greater general persistence across locations. Early flowering tended to correlate with higher yield and persistence of the cultivars across locations. Considerations on experimental conditions along with previous physiological studies from three sites suggested that water use efficiency of the cultivars tended to parallel their site-specific yield response. On the whole, the results suggest different adaptation targets, plant types, genetic resources and cultivar recommendation for northern Africa and southern Europe. Summer-dormant material of subsp. hispanica has prevalent interest for northern Africa. Breeding widely adapted, non-dormant or incompletely dormant Mediterranean cultivars of subsp. glomerata has prevalent interest for southern Europe, especially when targeted to moderate crop duration (3–4 years). However, completely summer-dormant germplasm could gain adaptive potential for Mediterranean-climate European regions in the future, to mitigate the effects of the predicted increasing drought due to climate change.