In some past works by the author and collaborators, the notion of ageing function of an exchangeable survival model was introduced and several properties of it were analyzed. Generally, the ageing function turns out to be a semi-copula. Here we focus attention on the special class of survival models whose ageing function is actually a copula. For pairs of models in this class we define a notion of duality. Such a notion can provide a better explanation of the analogies existing between the ageing function and the survival copula. The formulation of the notion of duality presented here came out some years ago, in the frame of research activity in collaboration with Bruno Bassan.