In the Cervidae, sexual dimorphism in body mass, armament and structure of the breeding pelage appears to be, as in African antelope, a curvilinear function on openness of habitat. Sexes converge in characteristics towards male‐like monomorphism in deer that hide in dense cover, as well as in gregarious, cursorial dwellers in open terrain. Relative antler mass correlates with weight dimorphism. The most cursorial species, the wapiti (Cervus elaphus canadensis) and the caribou (Rangifer farandus) converge towards male monomorphism, with the wapiti showing strong reduction in weight dimorphism (compared to red deer C.elaphus hippelaphus), and structure of the breeding pelage, but not in weaponry. Male and female caribou converge strongly in the structure of the breeding pelage, less so in weaponry, and least in weight dimorphism; antlers in female caribou are thus comparable to horns in male‐like females of plains bovids. In weight dimorphism, wapiti have almost reached the level of the African grazing antelopes of the tribes Alcelaphini and Orygini. Sexual dimorphism is maximal in mixed and concentrate feeders from semi‐open lands